On the edge of a frozen lake, somewhere outside St Petersburg, I am stretched out on the wooden racks of a rickety banya, or sauna. Clouds of steam part to reveal several lobster-pink Russians on the racks below. Some maniac has just thrown a bucket of water on to the hot stones in the corner, and the temperature – already somewhere between gas mark 8 and Dante’s Inferno – rises dramatically. I feel my bone marrow is melting. Meanwhile, my new best friend, Seva, is whipping me with birch twigs – “For improving circulation,” he grunts.

Russian banya are the Baltic equivalent of ginseng; they cure everything: liver complaints, skin conditions, muscle ache, sexual dysfunction, broken hearts, spiritual unease. They are an integral part of the Russian winter, for the thing about the banya is you need a freezing lake to get the full benefit. The door opened momentarily. Snow wafted in as two enormous men set off at a canter, clutching tiny bath towels, down an icy path to where a hole had been cut in the ice of the lake.

In our islands, most of us don’t get a great deal of winter. We get rough weather, especially this year, but not proper winters – frozen lakes, white sculptural landscapes, startling blue skies, snowdrifts groping the windowsills, a dry, sharp cold that crackles and snaps and presses your nostrils. In real winters, your breath plumes into the air like a steaming kettle, and the blood starts to pump. A proper winter is not just ravishingly beautiful, it is exhilarating. Winter is St Petersburg’s natural season. Perched on the edge of the Gulf of Finland barely 500 miles from the Arctic Circle, the one-time Russian capital is at its most beautiful when the snow starts to swirl. The Neva River is a wilderness of ice, and in the squares of black, bare trees the winter light is pale and watery. Along the frozen canals and the wide avenues there is a muffled stillness.

St Petersburg is the city where everyone looks fabulous in furs and rosy cheeks. As the afternoons draw in, the fat globes of the street lamps blossom along the Nevsky Prospect, and the frosted windows of the shops glow invitingly. In Theatre Square ballet fans hurry towards the brightly lit Mariinsky Theatre, where Nijinksy and Nureyev both performed; its season begins in autumn and runs through the winter. Across the city, frost patterns decorate the windows of the Winter Palace. Not far away, the great dome of St Isaac’s hovers like a vision in the early dark, while the statue of Peter the Great rearing on his horse above the bare trees carries a mantle of snow around his shoulders.

St Petersburg is not an old city, or an Asian one, like Moscow. It was built to be Russia’s window on the West. In the spring of 1703, Peter the Great, flush from victory over the Swedes, got down from his horse in the marshes that bordered the Neva River and cut two slices of turf with his bayonet. Laying them in the form of a cross, he announced, here there shall be a city.

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So began the 18th century’s most extraordinary building project. A quarter of a million serfs, soldiers and prisoners of war were press-ganged into Peter’s grand new project. Millions of logs were floated down the Neva, and stone work was forbidden elsewhere in Russia so that the nation’s supplies could be diverted here.

The Peter and Paul Fortress, where the Romanovs kept political prisoners in medieval conditions Photo: AP/FOTOLIA

The nobility was commandeered, too. A thousand of Russia’s best families were ordered to construct houses and palaces in the new city. In muddy fields and clapboard towns across the sprawling distances of Siberia, peasants listened to tales of how Peter was creating his city in the heavens then lowering it down to earth. Within 50 years, St Petersburg was one of the most sophisticated and opulent cities in Europe. Palaces and academies, cathedrals and theatres, ministries and state institutions lined the avenues and canals as they radiated from the golden spire of the Admiralty. Peter’s new capital, his window to the West, had turned its back on its creaky empire and on “Asiatic” Moscow.

Seva was born in St Petersburg and would never live anywhere else. I met him through mutual friends and he guided me around the city he loves. “Peter,” he said – he had the curious habit of calling the city by this single name – “we are always falling in love with Peter. It is a city of romance.” An artist, a bohemian, a romantic, Seva could have been the archetypal St Petersburg citizen.

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Real and imagined, romantics have always loomed large in Peter’s life. For instance, it was in St Petersburg that Anna Karenina fell in love with Count Vronsky . Tchaikovsky studied at the St Petersburg Conservatory and conducted the premiere of his Sixth Symphony in the city only nine days before his death; he is buried in the Tikhvin Cemetery alongside other St Petersburg romantics – Borodin, Mussorgsky, Rimsky-Korsakov and Dostoevsky. But it was Pushkin, the great Russian poet, who set the bar for gallant St Petersburg romantics, conducting numerous love affairs and fighting no less than 28 duels. He succumbed in the 29th, fatally injured by a man he accused of trying to seduce his wife. His seconds carried his body to his home on the Moika River Embankment. It was midwinter.

Fog envelopes one of St Petersburg's parks Photo: AP/FOTOLIA

Russian winters have made St Petersburg a world of interiors and, with 500 palaces in the city, many are magnificent. Step inside the double doors, shed the overcoat and fur hat, and you enter a world of sweeping staircases and gilded moulding, of forests of chandeliers and ballrooms measured in acres, of battalions of nude statues and regiments of headscarfed babushkas with mops trying to keep up with the cleaning.

In the Yusupov Palace, you can follow the assassination of Rasputin by the cross-dressing Prince Felix or attend a concert in the tiny rococo theatre.

The best of the palaces are a carriage’s drive from the city – Peterhof, Tsarskoye, Pavlovsk, the Catherine Palace. To see them in winter when snow drifts across the parklands is to step into the pages of a Russian novel – as we shall witness when the BBC’s spectacular adaptation of War and Peace airs tomorrow night (some scenes were shot on location at Catherine Palace itself).

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But the mother of St Petersburg’s palaces is the Winter Palace, a building that would make Buckingham Palace seem cramped. There are said to be 1,500 rooms and 117 staircases. Its excess reflected that of its creator, the Empress Elizabeth, daughter of Peter the Great, who ruled Russia for 20 years in the mid-18th century. Her wardrobes were said to be stuffed with more than 15,000 frocks while her floors were littered with unpaid bills. When construction costs ran 300 per cent over budget, she ordered a series of beer halls to be built across Russia to finance the shortfall, knowing she could rely on peasants to drink her back to solvency.

But let’s bypass the endless swank of Russian aristocracy and the stunning private apartments, many with a view across the Neva to the Peter and Paul Fortress where the Romanovs kept political prisoners in medieval conditions. Let’s head, instead, for the little museum tucked into several adjoining wings.

The Hermitage seems to reflect the scale of Russia – 6.5 million square miles across 10 time zones. Apparently you would need nine years to spend just a few moments in front of each of its exhibits, assuming you paused occasionally to eat and sleep. Catherine the Great was responsible for the nucleus of the vast collection; her artistic appetites seemed to be as impressive as her sexual ones. There are Egyptian collections, Near Eastern, Classical, Renaissance. But it is the paintings that really overwhelm – this is the largest collection in the world. Interested in Rembrandts? You will see some of his best work. Keen on Matisse? You’re in for a treat.

But it is winter: don’t get stuck indoors. Some of the best ice hockey teams are over at the Ice Palace. There is sledding, tobogganing, sleigh rides, cross-country skiing. And there are the Russian banya. Seva is an enthusiast. “Whatever is ailing,” he says, “banya is the cure.” We take a taxi to a frozen lake on the outskirts. A rickety hut is perched on the shore, with two tin chimneys belching woodsmoke. Disrobing in a side room, we follow an attendant through to the hot room. A couple of strapping women shuffle along a bit and Seva and I hunker down among the fleshy bodies. Despite the sweltering conditions, everyone is in a jolly mood and a woolly hat – the Russians believe extreme heat is bad for exposed hair.

The Petersburg plunge: winter swimmers prepare to take an icy dip Photo: AP

After 20 minutes of sweating like a self-basting turkey, I follow Seva outside into the Russian winter. Wearing nothing but small towels, we scamper along the frozen path to the end of a dock on the lakeshore. A set of steps leads down through the hole cut in the thick ice. A rope has been thoughtfully laid on so that we might have something to hang on to as our vital systems shut down.

Taking a deep breath, I lower myself into the water. For a moment I can’t feel anything; my body is numb with shock. Then the cold hits me, so cold that my body seems to be burning. We shoot back out of the lake as if there were a trampoline beneath the water and flee along the ice path to the enveloping heat of the banya. The endorphins are buzzing.

Back inside, Seva claps me on the back and smiles broadly. “Winter,” he says. “Bracing, eh?” That’s Russian understatement. Winter in St Petersburg is more than bracing.

It is beautiful, it is exciting and, down here at the banya, the sharp smack of a proper winter is absolutely exhilarating.