Nobel laureate Joseph Brodsky adored Venice. So much so that, starting in the early 1970s, he dropped in on the Italian lagoon city annually for 17 years, enigmatically describing his buoyant Eden as being “like Greta Garbo swimming”. Here the Russian poet would all but disappear, becoming “a small moving dot in that gigantic watercolour”.

However, Brodsky added, “I would never come here in summer, not even at gunpoint.”

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Lauded for centuries for its extra­ordinary prosperity, political stability and swagger, the Republic of Venice was historically called la Serenissima, or “the most serene”. Today, with more than 20 million visitors schlepping up and down its narrow alleyways and over its hump-backed bridges each year, applauding Venice for tranquillity is a little like commending Hong Kong as a travel bargain.

Usually stuffed to the gills (the perfect phrase – Venice is shaped, after all, like a fat fish), the watery wonderland is in crisis. Barely a month goes by without the remaining Venetians (there are now fewer than 50,000 permanent residents – about the same number as after the Great Plague of 1348) protesting at the shoddy treatment of their unique and fragile home.

In September, Venetians dressed up as pirates and took to small boats to confront the leviathan-like cruise ships that disgorge bovine hordes day after day. Weeks later, they lugged suitcases across town to symbolise being driven from their city by high prices. While Venice is famous for its glitzy film festival, these days concerned directors make doom-laden documentaries about the place (critically acclaimed The Venice Syndrome [2012] was described as a “portrait of a city in the process of destroying itself”).

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In short, visit Venice in the 21st century and you might leave not only with Venetian glassware souvenirs more likely fired in Suzhou than Murano, but also weighed down by guilt.

The trick, of course, is to do like Brodsky: alight on Venice only in winter, there to be greeted by “the smell of freezing seaweed”, which he declared synonymous with “utter happiness”. And what better guidebook than Watermark (1992), Brodsky’s petite yet personal paean to the strained Queen of the Adriatic?

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Poignant and dreamy, Watermark won’t tell you which chichi boutique property overlooking the Grand Canal is currently in with the luxe crowd, but it does capture how “in winter you wake up in this city, especially on Sundays, to the chiming of its innumerable bells, as though behind your gauze curtains a gigantic china tea set were vibrating on a silver tray in the pearl-grey sky. You fling the window open and the room is instantly flooded with this outer, peal-laden haze, which is part damp oxygen, part coffee and prayers”.

Brodsky would always visit Venice in December. This less accomplished writer prefers January (any time, in fact, between New Year and the witless pantomime that is Carnevale). This is when Venice exhales, scrubs off the fake tan and reveals itself. Without the crowds, suddenly Venice is romantic, magical, mysterious … all that you hoped for. And Venice in January is at its most affordable, with room rates at least halved from high season.

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But what to see in winter that cannot be appreciated in summer? Well … everything made visible by the sun – Venice’s low, weakened winter light has a pleasingly soft, hazy and cinematic quality (think filmmaker Nicolas Roeg’s spooky, dread-filled 1973 masterpiece Don’t Look Now). Fog rolls in off the lagoon, edges blur, buildings disappear, and water and sky merge. “On days like this,” Brodsky wrote, “the city indeed acquires a porcelain aspect, what with all its zinc-covered cupolas resembling teapots or upturned cups, and the tilted profile of campaniles clinking like abandoned spoons and melting in the sky.”

Like light, sound too becomes puzzling in winter (footsteps bounce and echo and amplify), and getting lost – common enough at any time of the year in labyrinthine Venice – takes on a mind-bending new dimension.

Stumble upon St Mark’s Square in fog and the brain fails to compute (“This can’t be St Marks; where are the people?”), and how many of us, when visiting Venice in summer, have given up on the idea of sinking bellinis like Ernest Hemingway – or chowing down on Scampi Thermidor alla Cipriani like writer Jan Morris (it’s her favourite, apparently) – at Harry’s Bar because the landmark eatery was (here’s that perfect phrase again) stuffed to the gills?

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Pop along in winter and you’ll get a table by the window. What’s more, the hole-in-the-wall bàcari (taverns serving Venetian-style tapas called cicchetti) favoured by the no-nonsense stallholders from the Grand Canal-side Rialto Market also suddenly have space for an outsider or two.

Believed to be the oldest bàcaro in Venice, cramped Cantina Do Mori dates back to 1462. It’s said that Casanova was a regular. Try the vinegar-marinated anchovies, the creamed cod and the house speciality of francobollo (“postage stamp”) sandwiches.

Speaking of Casanova, the legendary lover was addicted (or so says that lascivious legend) to hot chocolate, and the indulgent Venetian variety of the alleged aphrodisiac that’s served just off St Mark’s, at Caffè Florian (established in 1720), is richer than you’ll find anywhere else, a welcome treat when a bone-chilling wind rages down from the Dolomites.

And then there’s the dreaded acqua alta, when the canals overflow and water in St Mark’s can be knee-deep.

Not to worry: simply buy a stripy scarf to fend off the chill (yes, there is now an official gondolier-clothing shop, branded Emilio Ceccato and approved by the Gondoliers of Venice Association, next to the Rialto Bridge) and splash along to Libreria Acqua Alta (literally the “high water bookshop”) to browse the second-hand volumes piled in bathtubs and rowing boats to protect them from floods.

This, of course, is the perfect spot to grab your own copy of Watermark, there to find Brodsky’s opinion that historic Venice should be treated respectfully as a living, working city with a future.

“This city doesn’t qualify to be a museum,” the writer opined, “being itself a work of art, the greatest masterpiece our species produced. You don’t revive a painting, let alone a statue. You leave them alone, you guard them against vandals, whose hordes may include yourself.”