A teal-turreted hotel that affords knockout views of the lake, Badrutt’s Palace endures as St Moritz’s most magnetic address. Age-speckled mirrors hang above chess-board floors, favoured tables are reserved long into the future and you will spy notes from Sir Alfred Hitchcock and Ms Audrey Hepburn in the guestbook. The heady mood of it all quickly gets under the skin and, while nobody could blame you for wanting to stay put, outside you will find a 1968 Rolls-Royce Phantom – once owned by the British royal family – primed for off-the-cuff outings.

With miles of wide-open (and tremendously scenic) reds and blues for gentle cruising, plus a handful of near-vertical chutes down which speed freaks can fling themselves, sun-splashed Corviglia is the main event. Hop on an early lift to carve the first tracks on the just-groomed runs while the sun is still on its way up. Particularly great are the fast rollers that fan out from Munt da San Murezzan and, if the mood strikes, you can sharpen your turns on the flag-marked slalom course that descends beneath Plateau Nair.

An altogether different scenario awaits on north-facing Corvatsch. Here, the shadowy slopes offer up some of the most diverse (and demanding) terrain in the region and powder stashes stick around for days, unsullied. Along with pulse-quickening trails that plunge into dense fir forests, there is great off-piste territory to get stuck into (with the odd gnarly cliff jump, to boot) and beside the Murtèl middle station you will find kickers and rails for impromptu freestyle sessions.

Last but by no means least, isolated Diavolezza lures seasoned thrill-chasers who are keen to test their mettle. A tangle of unforgiving red and black runs trace their way down the largely treeless slopes, but it is the freeriding you are here for. With fierce winds and often excruciatingly low temperatures, few would want to tackle this terrain in a white-out, but the immaculate snowfields and endless opportunities for tricks off the crags and cornices make it an incomparably epic playground when the conditions play ball. Don’t miss the monstrous 1,000m couloir, and the ungroomed glacier descent down to Morteratsch couldn’t be better.

It will come as no surprise that life here revolves around the dazzling frozen lake. An evolving bill of festivals, races, revelry – and anything else loosely linked to the clinking of champagne coupes – unfolds year after year on the scene-stealing expanse. Following the Snow Polo World Cup is White Turf, where thundering hooves kick fresh powder off the glacial surface as Brunello Cucinelli-clad racegoers loll in deckchairs, shucking oysters and cheering. Then The ICE – essentially, an excuse to throw some of the world’s rarest cars, both old and new, around a makeshift track – amps up the horsepower further.

Standing face to face with Badrutt’s Palace on Via Serlas, Hauser & Wirth’s top of the world outpost feels more akin to a curator’s townhouse than a gallery. Close by is Galerie Karsten Greve, which is home to an equally astounding collection of contemporary works, from the slashed canvases of Mr Lucio Fontana to Mr Josef Albers’ square experiments.

Carving back towards more adrenaline-fuelled pursuits, you can don crampons for a morning of ice-climbing in the Bernina Gorge, which brings with it serious bragging rights, and why not hop on a sled and hurtle head-first down the Cresta Run? A dose of Swiss courage in the form of a Bull Shot (a sort of Bloody Mary, but with beef consommé) is encouraged.

Bringing its razor-sharp focus on seafood to the mountains, the sceney Milanese mainstay Langosteria resides in the CheCha hut on Corviglia’s Salastrains. Grab a sought-after table and surrender to the outstandingly good caviar and people-watching. Less splashy, but packing just as much punch in the taste stakes, rustic Chasellas dishes up palate-pleasing sustenance, from crispy fried egg-topped röstis to Engadin sausage with sauerkraut, on a buzzy terrace next to the Suvretta-Randolins lift. Down in the town, Super Mountain Market is the go-to spot to knock back an espresso.

Michelin-starred Krone delivers a modern riff on Italian flavours with its stellar tasting menu – the wine list will satisfy even the most finicky oenophile. Occupying Chesa Veglia’s pine-clad hayloft, Pizzeria Heuboden draws a faithful horde of locals and visitors for whom its truffle-heavy dama bianca has become something of a religion. A short drive out of town in under-the-radar Zuoz, you will find old-school Dorta, where cockle-warming Grisons classics are served beneath beamed ceilings.

After going hell for leather on the mountain, few things are more satisfying than settling into a shearling-strewn bar and diving into a curative vat of Alpine liquor. Paradiso Mountain Club & Restaurant hits the spot, drawing a ski-and-be-seen crowd of revellers to its sun-licked terrace, where deep house cuts set the tempo. Order a round of flaming cognac-spiked Parapampoli to help soften the stupendous views and bask in the last rays of the day.

Slap bang in the middle of town, you’ll find Café Belmont, a low-lit wine bar with conversation-starting artworks on the wall and a great menu of sharing plates. Round the corner, Pavarotti & Friends is another winning late-night spot. Relaxed evenings erupt into raucous on-the-table dance-offs – rumour has it the owner occasionally bursts into ebullient song. If you’re still standing (bravo!), the famously exclusive Dracula Club is a St Moritz institution where carousers cut shapes to throwback classics beneath a dazzling garlic clove-shaped disco ball.