Christmas is coming, the goose is stepping off the bathroom scales thinking, "hmmmm, must go down the gym"; the winter nights are drawing in, that annoying ad with Richard E Grant and Julia Sawalha is never off the television and rows about which set of in-laws you're spending Yuletide with have already kicked off. And there probably won't be any snow. When the big day dawns, we won't be looking out at a magical winter wonderland, but at our dank, rainy back gardens.

So, in search of a real White Christmas antidote, I spent a strangely funky weekend with my girlfriend in the Finnish capital of Helsinki, where snowy magic really is guaranteed. (And, as it happens, it's a city in which I hope interest will be re-awakened here, as Helsinki is the setting for the brilliant new film, The Man Without A Past, by the Finnish master Aki Kaurismaki.)

Over the Friday-to-Sunday we were there, it did not cease to snow: a fine delicate downpour of flakes lending a crystalline beauty to the trees along the main shopping avenues: the unpronounceable Mannerheimt, the Pohjoisesplanadi and the Uudenmaankatu. In fact, sometimes the snow can ease off a little, but then a gust of wind will take it off the branches, engulfing you out of nowhere in a swirling, powdery mini-blizzard - an oddly sublime experience.

Finland was ruled by the Swedes for 700 years until the beginning of the 19th century, and then by Russia until 1917 - after which it was independent. So there's a distinctive mix of Scandinavian and Russian in the culture and cosmopolitan style. For many years during the cold war, film crews used Helsinki to stand in for Russian cities - Gorky Park, Doctor Zhivago, Reds - and the city does markedly resemble St Petersburg.

We marched out into the bitter cold on the first day - the temperature never rises above zero at this time of year - wearing so many thermal padded layers that we resembled Mr and Mrs Michelin. At rest, our puffy, tubular arms stuck out from our sides like the wings of Thunderbird 2, and our thermally-padded trouser legs rubbed squeakily together as we walked, an activity requiring a sort of lateral hip-swivelling motion. We first took in the very wonderful Lutheran cathedral, the Tuomiokirkko, in Senate Square and then walked over to the equally beautiful Russian Uspensky cathedral. The tour constituted a brisk - very brisk - one-hour walk around the centre of town, after which it was time for lunch.

Lappi is a zany Lapland restaurant in which reindeer is served smoked, braised, grilled, and maybe even poached. I elected to have the Lappish crumbed cheese - a slightly stodgy concoction, to be frank. And to drink? With a poker face, the waitress directed my attention to something called a Reindeer's Tear. "What's in it?" I asked, my pink cheeks and nose glowing naively. Still deadpan, the waitress merely referred me to the menu description which was: "An unconstrained drink". My girlfriend wisely opted for a cranberry juice, which arrived in a large tumbler, but mine was in a tiny shot-glass in which there was what really did look like a large opalescent tear-drop with three cranberries floating in it.

Incautiously, I took a biggish gulp. For some microseconds, nothing happened. Then it seemed as if I had been noiselessly, but with tremendous force, hit over the head with a shovel. After that, I heard a chorus of little birds twittering the opening theme to Jean Sibelius's Finlandia symphony. A Reindeer's Tear costs 5 euros. For 10 euros, presumably, you can have a Reindeer's Anxiety Attack; for 20 euros, a Reindeer Slaps Santa And Storms Out; and a 50 euros' jug will get you a Reindeer Checks Into The Priory.

There is, in fact, a sort of Reindeer-oriented mini-tourist-economy in Helsinki. You can buy slices of blood-red reindeer meat and, nothing being wasted, reindeer pelts on which one presumably reclines in highly incorrect and indeed unChristmassy style in front of one's enormous log fire after the sauna, Reindeer's Tears cooling on the back doorstep.

In the afternoon, it was time for the deeply entertaining National Museum of Finland. As the guidebooks candidly concede, this is a bit meagre because Finnish history is distinctively thin on the ground. In the 20th-century section, there is a glass case earnestly dedicated to what modern young Finns look like wearing T-shirts and jeans. There's a display case of typically Finnish groceries, including a box of Weetabix and Nescafé. A room called Utbildade Finlandër, or Educated Finns, shows a complete classroom with chalkboard and desks. Another room called Lycklig Vardag, or Happiness In Everyday Life, displays a collection of bicycles, sledges and prams.

I was disappointed that there was no tribute to the men's fashion item that was everywhere on the streets. It was all very well the museum showing off the array of pert 21st-century backpacks for young people which are the size of 10p coins. But where were the jumpers? The folk of Helsinki are much tougher about the cold than we were on our trip - old and young alike went about in the snow with open anoraks and no hats, but the menfolk certainly like their jumpers. These are decorated in the traditionally appalling fuzzy designs, all zig-zag lines and playful little motifs, reminiscent of Man At C&A from the 1970s.

But no visit to Helsinki, I was assured before arriving, was complete without a visit to the Yrjönkatu Swimming Hall: an old-fashioned sauna and swimming centre. It was men only on Saturday, and women only on Sunday. So I went first, with my trunks and goggles rolled up tightly under my arm. It really is a beautiful Roman-style colonnaded pool over which people gaze from a second-floor gallery.

There was just one thing. I should have guessed, but I didn't. The awful truth dawned on me as I saw my fellow bathers: swimming in the nude was very much the order of the day. Had the pool employed the PE master from my old school, I wondered? Had they all forgotten their kit and been made to swim nude? No, they all clearly loved it: lots of great fat Finns wobbling unselfconsciously about in the altogether. A number of similarly unclad customers posed above at gallery level. The entire effect was as decadent and homoerotic as a Ryvita biscuit.

Strangely, there was a woman attendant present, her chin cupped ruminatively in her hands, unmoved by the spectacle. A naked Finnish man sashayed up to her at one stage, to weigh himself on the machine just by her chair, chatting amiably. I, however, did my 30 lengths wearing a pair of stout British trunks. My partner was equally discomposed when she went the next day. "All those enormous breasts!" she said. Jesus. Surely not as enormous as the ones that I saw?

The nightlife is, as Peter Sellers said in his Balham travelogue, awakening. You can check out a bar called Leningrad Cowboys co-owned by Kaurismaki and his brother. Very lively. In the evening, we ate Russian at the classy Alexander Nevski restaurant - reputedly the most expensive joint in all Finland, but it cost only about as much as a reasonably pricey London dining room. There was much melodramatic flambéeing at the table. A classical-guitarist wandered about, serenading. They like their karaoke, do the Finns, and many insisted on contributing a hoarse vocal to whatever he was playing. His dreamy, bittersweet instrumental version of Autumn Leaves began to sound like something you'd hear at the Clock End at Highbury. After a bit of a Reindeer crying-jag, I actually took the guitar from him and tried, with many a vulgar glissando, to play the opening bars to a Villa-Lobos study that I remember from my Grade-Five lessons at school. He took it very well, considering.

Taking taxis everywhere reminded me of the Helsinki segment of the Jim Jarmusch film Night On Earth, about five taxi-rides in five cities. The Finnish segment showed a taxi-driver deeply oppressed by the tragic anguish of life's choices. Well, the real ones are not like that, any more than New York cab drivers mutter about a real rain coming to wash all the scum off the streets. But it's not hard to imagine a stoicism, a melancholy reserve in the Helsinki taxi driver that comes at least partly from driving around in the freezing cold weather all the time, weather that in deep midwinter is compounded by almost total darkness.

Then it was back to our hotel, the Torni. It is a lovely place ( torni means tower), designed in 1930. Like so many buildings in these parts, all its doors open outwards, an oddity that takes some time to get used to. The Torni actually has a place in popular myth in Helsinki, as it was where top Soviet brass were billeted during the war. Finns, who were habitually suspicious and resentful of their former imperial masters from Russia, made sure to watch their tongues around the place. Whenever advising discretion, people of a certain age apparently say: "Shhh - keep your voice down at the Torni!" Puzzling if you're not prepared for it, though I must say it was rather quiet in the lobby.

The Torni's biggest selling point is the Ateljee Bar, right at the top, on the 13th floor, accessed by lift and then a spiral staircase. There, we had cocktails, looking out over the beautiful Helsinki night sky. On a clear day, the barman reverently told us, you can see all the way to Estonia.

· The Man Without A Past is released in the UK on January 24.

Way to go

Getting there:

British Airways (0845 7733377, ba.com) flies Heathrow-Helsinki from £204.50pp return including flights. Travelscene (0870 7779987, travelscene.co.uk\) has two nights' B&B in Helsinki from £235pp including flights.

Where to stay:

Hotel Torni (+9 131 131 sokoshotels.fi/english/index.cfm) superior double room for £108 per night.

Further information:

Finnish Tourist Board, PO Box 33213, London W6 8JX (020-7365 2512, finland-tourism.com).

Country code: 00 358.

Flight time Heathrow-Helsinki: 3hrs.

Time difference: +2hrs.

£1= 1.51 euros.