Lars Horntveth is not a fisherman. He might be standing on the deck of a former whaling trawler deep in the fjords off the coast of Tromsø in Arctic Norway, his mildly receding hairline blown almost upright by unforgiving blasts of wind, his coat spotted with snow, but though this is skrei fishing season – the period between January and March when cod migrate through the area in order to spawn – he's here for another reason altogether. He's here to sit in a hot tub on the deck of a boat that's been turned into a floating spa, then in a sauna that offers a view at sea-level out across the Norwegian sea, and finally a Turkish Hammam in the hold that also contains a tiny pool filled with freezing water drawn from the ocean below in which to cool off when the steam gets too intense.

Lars needs a break. A few nights ago in Bergen, the multi-instumentalist completed work producing and mixing the new album by Martin Hagfors, an American born, Norwegian folk-rock artist, the party lasting late into the night. "Actually," he corrects himself, "late into the morning". Two nights later, back in Oslo, he celebrated Susanna Sundfør's victory in the Best Popular Music Composer category of the Spelleman Prize, Norway's equivalent of the Grammys, having produced her record, The Brothel. Much of the last year has been spent touring with both Jaga Jazzist and Sundfør through Scandinavia, Europe and as far as Japan, and what little time he's had back at home has seen him composing music for two radio plays, one to be broadcast at prime time this Easter. So now, after an early start in Oslo, blood pounding in his ears following the afterparty for the Spelleman last night, Lars just wants to sweat his hangover out and get some rest. "It's my own fault," he groans. "Too much Aquavit. Too many spirits."

Lars may not be a fisherman, but he's one of Norway's busiest musicians, and as a founder member of Jaga Jazzist, the unconventional, genre-busting collective whose last album, One Armed Bandit – released by Ninja Tune a year ago and heralded on this site for "effortlessly mix(ing) inventiveness with accessibility" - he's rapidly becoming one of the country's most thrilling musicians. Having formed the band in 1994 at the age of 14 with his brother Martin, they have slowly but surely earned an enviable reputation across the globe for their unusual but groundbreaking instrumental sound, something Lars calls – a grin teasing his lips – "progressive electronic jazz rock music".

For more than half his life (he's 30 now) the band have recorded hard and toured hard, with A Livingroom Hush voted Best Jazz Album by the BBC in 2002. And even though they took a five year break between the release of 2005's What We Must and 2010's One Armed Bandit, it wasn't like they were standing still. The two Horntveths continued to play together in The National Bank with Thomas Dybdahl, Morten Qvenild (from Susanna & The Magical Orchestra) and Nikolai Eilertsen (of Big Bang and Elephant 9), while Lars also performed on Hanne Hukkelberg's Rykkestraße 68, composed for Diskjokke, provided string arrangements for former teen star Marit Larsen's solo debut Under The Surface (another Spelleman Prize winner) and remixed Four Tet. Somehow, in 2009 he also found time to release his own solo album, the spellbinding, neo-classical Kaleidoscopic, a 37 minute piece featuring the Latvian National Orchestra. The guy deserves a rest.

"I'm constantly working," he confirms. "I have this stupid thing where I get a bad conscience when I'm not. It's in my mind seven days a week. I always try to get rid of that feeling because it's not healthy working all the time, so me being on a trip like this is really good. Just knowing that you have four days off, it's great."

Over the next few days he makes a fair stab at unwinding. He soaks in the hot tub in a woollen hat, declining the beers clutched tightly in the hands of other passengers from lunchtime until the small hours. He roasts himself in the Hammam until his skin is puce, then lowers himself tentatively into the freezing pool, only to emerge into the fog once more. He endures prolonged bouts in the sauna as the monochrome mountains pass by the windows, emerging briefly on one memorable occasion in just a towel to take charge of a fishing rod for a brief burst of angling amidst a howling gale. Finally, when the Vulkana, our trusty vessel, has docked back in Tromsø, he sits down to nurse a pint of Mack in Driv, a timber-framed bar located by the harbour of this small picturesque city. As if to emphasise the amount of time he's spent working these last sixteen years, he's interrupted on three separate occasions by the sound of the bar's stereo playing records in which he was involved. "That's me!" he announces excitedly at one point as a saxophone solo floats through the room. "That's my Clarence Clemens saxophone! That's my alter ego!"

Thanks to his various projects, however, Horntveth has plenty of alter egos. So what is it that makes him, and indeed Norwegian musicians in general, take on so much work? Could it be that in their smaller communities there's so little to do? Is it perhaps the long winters?

"We're in Tromsø now," he replies thoughtfully by way of example, "where the whole electronic scene grew up: Røyksopp, Mental Overdrive, Rune Lindbæk, Bjørn Torske, Biosphere. Those guys are from Tromsø, and of course it's dark here all the time - well, most of the time - and I think that's quite true of the rest of the country as well. Norwegians haven't really had much international success, so we try to make... not more advanced, but maybe more unique music that is not supposed to be played on the radio. It's more niche. So I think there are many Norwegian acts that have tried to make it in a smaller scene. For example Jaga Jazzist: we have this kind of music that you can play everywhere in the western world, actually playing to quite a good audience because there are always people that like electronic music and post-rock and jazz and jazz rock, and that kind of smaller niche."

He takes a sip of his beer before continuing.

"Once you're trying to go outside Norway with a more pop related sort of music, maybe with vocals, it's extremely difficult. You have so many other acts doing the same thing with much better lyrics! There are exceptions of course, but the only international success we have is A-ha, which is a really big thing but it's an old thing. And A-ha was signed to an English label and an American label, so we've never had the economic side of things that Sweden has, all those exports. But we have quite a lot of those niche acts: the black metal scene, the electronic scene and the jazz scene since the 70s. I guess 80% of the ECM records are recorded in Oslo."

Where some countries are recognised for a particular sound, though, Norway doesn't really have a definitive style. A country like Iceland has successfully marketed itself as the home of all things epic or kooky, with bands like Sigur Ros defining a musical version of the awesome barren landscapes of the countryside, adopted by a succession of fellow countrymen since, and Bjork trilling eccentrically in a contrasting but equally otherworldly fashion. Norway's environment is similarly dramatic, but the results are less easy to categorise.

"I think you can hear with many Norwegian acts that they're from Norway, especially in the jazz scene, that they have some kind of melodic, Nordic thing going on," he contends. "With Jaga I try to steer away from it, but I grew up with ECM Records and all that stuff so it's in our system. And here in Norway it's really hard to get on the radio without being really nostalgic. Everything has to be kind of depressing to be popular."

There does seem to be a certain authenticity to the music that the country produces. Whether one thinks of the organic nature of Norway's electronica, the wooden cabin atmospherics of its country music, the brutal starkness of its metal scene or the innovative and influential lines of its jazz, it's often hard to shake off the feeling that it's come from the heart.

"Of course we have good pop acts too," he argues, "but the stuff that's more important for international audiences is more authentic. We've been talking about this for ten years at least, why the Norwegian scene is special in that way compared, for example, to Denmark and Sweden. And I guess I have to say that we don't have confidence in being really popular. If we had that, I guess we could have had some really great pop acts as well, but it's probably easier to be more authentic."

One of the interesting things about the country is the fact that it seems to cling to traditions without a great deal of shame. Once a year, on Constitution Day, May 17th, the inhabitants of the country's cities, towns and villages dress up in their bunads – the traditional rural costumes – to attend parades with marching bands or attend alcohol-fuelled picnics. While this might not be embraced across the board, the day is celebrated with a fervour that would perhaps be alien to, for example, the British, whose national pride has been largely hijacked by the far right. Music, too, seems rooted deep in the nation's heart, so much so that the inaugural Nordic Music Prize at this year's by:Larm – the Nordic equivalent of South by South West – was awarded by the country's Crown Prince. It's hard to imagine a comparable sight on our sceptred isle to that of Jonsí landing a smacker on royal cheeks. Britain still seems gripped by the values of punk rock, or – as Bono gushingly put it – the sense that all you need is "three chords and the truth". But, in Norway, being musical doesn't seem to be anything to be embarrassed about. Lars, however, isn't so sure.

"When we released the first National Bank album, we knew that there was going to be the stupid supergroup bullshit thing, with people from these different bands forming, and they really have 'a remarkable career' behind them and 'really good instrumental skills'. That's not a popular thing at all. When we released the album we did everything ourselves: we paid for the whole thing and sent it to the record labels without telling who the band was. We wanted a confirmation that we had something that they actually wanted to listen to, not that they wanted to sign the names. So it's the same thing in Norway with being skilled musicians, but it goes in ebbs and curves.

"For me it's silly, because I have no musical education at all. I'm self-trained. But a few years ago, there was a big thing in Norway with soft rock – you know, Crosby, Stills & Nash, Steely Dan, and Toto and all that bullshit – being really popular again." He shudders. "Yeah! Now suddenly Toto is really cool! But after that scene quietened down a little bit, it's a little more accepted to be, or trying to be, progressive or trying to do something that is not like The Ramones or straightforward rock."

So suggesting that there's a common theme running through all the country's music is arguably as futile as insisting that all Norwegian males are weather-beaten, bearded, rugged outdoors types when clearly the country has its fair share of delicate skinned intellectuals. Early on during this expedition, the boat came to a halt to allow those inclined to swap the steaming saltwater of the hot tub for the icy waters of the Norwegian sea. A number of passengers leapt naked into the aquamarine depths before scrambling back up a ladder onto the deck. Far more, however, remained heavily wrapped up, shaking their heads in disbelief. So how easy is it to stereotype a Norwegian?

"I know a few people who do that kind of stuff," Lars laughs as he recalls the Arctic plunge incident, "but it's just a few. Of course, I'm hanging out with musicians and artists and ‘feminine' people, but you have that as well - the macho attitudes - though I don't see that much of it. I think it's there, but it's so funny being on that boat now and seeing how few are doing that macho stuff. There's not much manliness there, but it's fantastic to be with people who actually enjoy that stuff. I don't have so much courage. I think for people from the south of Norway, it's not a common thing to do. I don't see a lot of that in general in Norway, and I don't see the point. Of course in the steam bath it was fantastic. But I don't want to be killed!"

Nonetheless, Norway is an astonishing land, full of breathtaking scenery, vast mountains, crystal clear fjords and a joyous purity throughout its countryside. It must be hard not to be influenced by the place in some ways, even if the results are enormously varied and fail to pander to stereotypes.

"I'm a more unromantic guy when it comes to inspiration," Lars counters. "For me, it's about having a project that I really want to do something with. It's very unromantic, the way I work. I'm working with different projects all the time, so my inspiration is that I'm trying to do the opposite of the previous thing I did. I guess it doesn't sound like it, because that's extremely difficult: to make something that's a total opposite. But it's a good thing to have in mind: to try to expand. One thing that really inspires me is to do something that's really embarrassing, stuff that you have hated before yet try to do: to play that instrument, to play that thing that you've really hated and make it your own."

It's perhaps precisely for all these reasons that Jaga Jazzist are so fascinating. They are as impossible to pigeonhole as the music that is emerging all around them, refusing to be tied down. Throwing in an extraordinarily diverse mixture of influences – from Tortoise's post rock to Morricone's soundtracks, from Gil Evans' jazz to Tony Allen's afrobeat, from DJ Shadow's beatsmithery to Funkadelic's grooves – they confound and inspire in equal and ever increasing measures.

"That's the thing now with Jaga Jazzist," Lars concludes. "Every one of us is making albums, producing albums for other people, playing on other people's albums. It's quite a big group of people, like maybe twenty people, that has been through the Jaga system. We have this brand with Jaga that we've worked on sixteen years. So I think that's very important, that you have your own musical style, that you always try to expand, of course, but you have your band and you keep that group together and make it more and more interesting."

And as the snow continues to fall, he downs the last of his pint, steps outside for a cigarette, then heads back to the boat. Though it's one of the last nights he'll have to kick back, Lars Horntveth, like Jaga Jazzist, can't sit still for long, and he's got another surprise in store. Rolling up his sleeves, he gets to work in the Vulkana's kitchen alongside Joakim Haugland, the boss of his Norwegian label Smalltown Supersound, to whip together a four course meal: cod's tongue fried in garlic, marinated halibut, sardines in lemon juice and risotto with salted cod and carrot. The combination is extravagant, unexpected, exotic, absurdly good and – perhaps, finally – definably Norwegian. The time off has done him good. But the rest is still unwritten.

There are a small number of tickets left to see the superb Jaga Jazzist at London's Scala on Wednesday night