Live-in art: Detail from the reconstructed hut at Hjertoya

Artist Kurt Schwitters' live-in sculpture still lures pilgrims to the fjords, says Charles Darwent

In the summer of 2003, Terje Thingvold was showing a visitor around a hut on Hjertoya, an island in the Molde fjord in west Norway. The man, stumbling on the dirt floor, fell against the door: the blow dislodged a piece of wood about 18 inches by five. Thingvold was aghast. In the 1930s, the hut had been the summer home of the German-born artist Kurt Schwitters. As at his apartment back in Hanover, Schwitters had turned the one-time potato barn into an artwork – a three-dimensional, live-in sculpture he called a Merzbau, or Merz-construction. The stumbling man had broken a bit off of Dada's Sistine Chapel.

Unusually for Schwitters, this story has a happy ending. Fingering the sliver of wood, Thingvold traces an inscription, pencilled in German: Viel Glück für uns in Norwegen! – Good luck to us in Norway! It was written by Schwitters himself, in the first summer he spent on Hjertoya with his wife, Helma. Once inscribed, the fragment was glued, writing-side in, to the hut's wood-lined walls. (For Schwitters, a tireless raider of bins, his favoured building material was the margarine box.) For three quarters of a century, until the stumbling visitor revealed it, the message was lost to the world.

Thingvold points to other inscriptions on the walls. One, illegible, was recently decoded: it turned out to read, "Do not leave sugar in the barn over the winter." Not all the master's writings are gems. Still, standing in this cramped space, snow deep against its windows and your breath freezing in clouds, you sense Schwitters at your side – all 6ft 4in of him, dressed in tweed and knickerbockers, with the long-suffering Helma at his side.

Even if you are a Schwitters fan – and if so, you join Zaha Hadid, Damien Hirst and just about every groovy artist and architect you can name – the hut on Hjertoya (pronounced yah-toy-ya) will probably come as a surprise to you. Insular as we Brits are, we know about our own Merzbau, near Ambleside in the Lake District. That so-called Merz Barn will play a major role in the Tate's forthcoming show, Schwitters in Britain. We are unlikely, though, to know its precursor – the place where we're standing now, where Schwitters spent his happiest times.

From outside, the dry-stone-walled Schwittershytta looks like its English equivalent. (Ours was the fourth and last Merzbau. The first, in Hanover, was destroyed by RAF bombing in 1943; the second, near Oslo, burned down in 1951; Hjertoya's was the third.) Schwitters hadn't wanted to leave for England – "Do you remember it, our beloved Hjertoya?" he wrote sorrowfully to Helma from internment on the Isle of Man – but the German invasion of Norway in 1940 forced him to flee. Nazi taste in art did not stretch to the bus-ticket collages and crazed sound symphonies that had made Merz famous.

You can imagine Schwitters' joy when he glimpsed his hytta's twin in a Cumberland wood.

Inside, though, similarities end. The English barn began to decay soon after Schwitters' death in 1948. Soon, the only sign of him was one sculpted wall, removed to a museum in Newcastle in 1965. Despite the extremes of Norwegian weather and an unlocked door – Terje Thingvold recalls playing in the hut when he swam at Hjertoya as a child – the Schwittershytta survived relatively intact. True, most of Schwitters' plaster nooks and niches melted away before an open window was filled in in the 1970s. But Thingvold's torch picks out keel-shaped hollows, the skeleton of a structure whose coloured remains – a yellow and blue lintel, jagged shards of red-painted wood – call up the ghost of what was there.

On the walls, still, are scraps of paper – pages torn from 1930s art magazines, yellowing ads for a paint called "Alf", ferry timetables – glued there by Schwitters in his effort to turn the potato barn into a three-dimensional collage. And then there are the margarine boxes. "With these I built our happy home," he later wrote. Thingvold, on hand when the stumbling man revealed Schwitters' good-luck message, feels there are other secrets behind them.

He'll soon know. Back in Molde, the town's museum, the Romsdal, is about to close. When it reopens in 2015, the contents of the Schwittershytta will be moved into its spectacular new building: they will be joined by a collection of the work Schwitters made in Norway, including the hytta's collaged door, currently at the Henie-Onstad Art Centre in Oslo. (A visit here is a must if you're passing through Oslo en route to Molde.) Schwitters is too big a name these days to be left in a damp potato barn on a small island in a fjord.

Although conservators have tried to stabilise the hut on Hjertoya, there is little that can really be done. Damp stone walls and margarine boxes are not a good mix; even less so, damp stone walls and paper. And then there is the question of access. When Schwitters died in Ambleside in 1948, his death went unannounced. Now, he is hailed as a founding father of modern art, the man whose Merz-art led to the likes of Robert Rauschenberg. Schwitters has a cult following, many fans.

So, if you can, go to Hjertoya soon. A ferry runs the mile across the Moldefjord in the summer, tracing the route that Schwitters took in his rowing boat. Although the hytta is closed to visitors, you can still look through its windows at the relics of the Merz masterpiece. In a nearby farmhouse, once the home of his landlords, the Hoels, is a display of the portraits and landscapes Schwitters painted to make ends meet. (Perennially broke, he swapped these for shoe repairs and hot baths at a Molde hotel.) On the wall, too, is his First Hjertoya Symphony, written in a phonetic Norwegian he didn't understand in imitation of Mr Hoel talking to his dog, Vamos: "Nobody is like Vamos/That dog of mine!/He is so good/He is so lovely/He is so small!" Mutter it aloud to yourself: it makes a strange sense.

Travel essentials

Getting there

Charles Darwent flew from Heathrow to Molde via Oslo with SAS (0871 226 7760; Return flights start at £130. Alternatively, Norwegian Air Shuttle (00 47 21 49 00 15; covers the same route to Molde from Gatwick and Manchester.

Staying and seeing there

Rica Seilet Hotel, Molde (00 47 71 11 40 00; Doubles from Nk1,940 (£218), including breakfast.

A free hourly shuttle bus runs from the Thon Hotel Opera in Oslo (00 47 24 10 30 00;; doubles Nk1,576/£177) to the Henie-Onstad Art Centre (00 47 67 80 48 80;

More information

Schwitters in Britain is at Tate Britain from 30 January to 12 May (020-7887 8888; Admission £10.