Lying so still as to appear dead, I see the shark swim silently towards me. The length of a Cadillac, its silent blue form floats past, circles, and slowly returns. In my warm stupor, I reach out to touch his slick slippery skin – just once, before it's all over. For over it must be: I have a gemstone glycolic peel facial booked for 5pm. Wild horses won't keep me from that.
It takes the effort of Hercules to haul myself off the personal waterbed and into the treatment room. The chill-out zone at the Aquagranda Livigno Wellness Park spa – with its individual gel-filled beds surrounded by giant deep-sea images projected on to art-installation walls – is just one of Livigno's affordable entertainments. The space-age concoction of water, glass and plastic-fantastic was designed by the Italian architect Simone Micheli, who must have watched a lot of The Jetsons as a kid. It's the après-ski antidote to a day of high-Lombardy sun, wind and snow.
And snow is on the menu in Livigno, a series of three linked hamlets peppered with old barns and rustic stone chalets. The name derives from the old German for "avalanche". Tucked in a sunny transverse valley running east-west, it's a little over three hours from Innsbruck airport via Switzerland. You reach Italy through a one-lane tunnel. In March, the mountain-top snowpack is an impressive three metres, requiring the tall to duck when skiing beneath the chairlift. Yet despite Livigno's sound snow pedigree (it's nicknamed Little Tibet, due to its cold and lofty perch), this Italian resort is still off the radar of the average British skier. Perhaps it's too cheap.
A buon mercato, a basso prezzo: one of the quirks of Livigno is its tax-free status, bestowed originally by Napoleon and maintained into the 21st century. Around 200 shops sell cheap alcohol, cigarettes, perfume, electronics and luxury goods along the long main street, generating a vibe of al fresco departure lounge as destination. It doesn't stop there: low prices are reflected in the bars and restaurants lining the 10km strip. There is a Michelin-starred restaurant, Ristorante Mattias, but most places to eat are small, low-key and casual.
To add to the charm, the heavy-shopping Europeans tend to ski fewer hours than us, so, unlike the snow, Livigno's lift lines are thin on the ground. For those who love to rack up the miles, skiing here is a non-stop love affair on slopes that rise above both sides of a wide valley, like two giant slices of a ciabatta sandwich waiting to be devoured.
Bordering Switzerland's Bernina range, the Carosello side offers the most skiing, accessed by a gondola or a series of chairlifts from the village. Sun pours over rolling pistes, groomed to make everyone feel they're levitating above the snow, expending no visible effort at all.
It's red-run heaven, above the treeline and within the comfort level of almost any skier or boarder. And the 115km of mostly wide intermediate terrain is easy to advance on to from the beginner drag lifts that line the valley floor. Indeed, there's a good incentive: 12 of the area's 30 lifts are drag lifts, many of them servicing the beginner areas. After a day or two of T-bars, novices will be relieved to take that snow plough on the road.
In this part of northern Lombardy, the road and the piste inevitably lead in one direction: lunch. A proper example is found at the lovely table-service restaurant at the mountain-top Carosello restaurant. Beginning with hub cap-sized heaps of cured ham, cheeses and pickles, we move on to pizzoccheri, the fresh buckwheat pasta drenched in magnuca cheese, accompanied with superb local red Nebbiolo wine. The harvest of these grapes is an extravagant affair: like spoilt skiers in search of perfect powder, when the steep, terraced vineyards of Valtellina become too precipitous for the pickers to tackle on foot, they call in the helicopters.
Stuffed like fat ricottas, it's time to waddle back blinking into the sunshine to tackle the other side of the valley: the 2,785m west-facing Mottolino. OK, first we make a brief stop on the sun-drenched terrace for a Bombardino, the million-calorie egg liqueur that is the region's signature drink. This is strictly for the journey, since, in order to reach the other side, you must factor in a five-minute taxi (€6) or the bus (free).
Up on Mottolino, there is more to interest better skiers and boarders: a big fun park with jumps and pipes, and the area's only two black runs. While experts won't find much diversity on piste, the Trepalle area beneath Monte Della Neve has some good off-piste routes. Livigno has also styled itself an Alpine telemark capital, hosting an annual free-heel festival every April, and is known for its ski-touring terrain. It's possible to ski-tour all the way to Bormio, with the Ortler sparkling in the distance, across some spectacular scenery.
After a short afternoon's skiing the following day, we drive for half an hour towards Bormio, across one of Europe's highest permanently inhabited parishes. Our destination is Husky Village, buried in the lost and wild valley of Alta Valtellina. This area was once host to one of the most thrilling laps of the Alpirod – a now-defunct sled dog race that crossed southern Europe in several stages. Its name was adapted from the original (and surviving) Iditarod race in Alaska, founded by Joe Redington Sr. The owner of Husky Village, Lorenzo Tilli, worked as a handler for Redington. A decade ago, Tilli brought six huskies from Alaska to Italy. Today, non-pros can mush their own sled pulled by teams from his pack of nearly 50.
"Our dogs are fully trained," the brochure promises – so that we don't have to be. Which is lucky: though the bulk of the route consists of miles of flat tracks, there is one wild 180-degree turn where you too may learn what it feels like to see your blue-eyed ships of the snow running away from you hell for leather, barking for Italy.
Four legs-good culture continues at Latteria di Livigno. We tour the factory, and watch milk become cheese, butter, yoghurt and – best of all – gelato, before our very eyes. Milk is collected daily from the valley's 125 small farms, purely for local consumption since the town's special tax makes its produce too expensive for export.
It's all there to be enjoyed. A dozen flavours, for €1 per luscious scoop. In Livigno, ice cream is just one of many guilt-free treats to relish on a holiday that won't leave you destitute – and just might have you heading home in a waft of Hermes scent, with a Moncler jacket on your back.
* The writer travelled to Livigno with Inghams (020-8780 4447; inghams.co.uk) and stayed at the four-star Hotel Intermonti. The price starts at £729 per person for a week's half-board, including flights from Stansted to Innsbruck and resort transfers. Flights are also available with a supplement from Birmingham and Belfast. Inghams offers a ski saver pack, including a six-day whole area lift pass, six days' superior ski hire and three two-hour sessions of tuition for £169 per person.
* Livigno: 0039 0342 052 200; livigno.eu
* Aquagranda Livigno Wellness Park: 0039 0342 970 154; aquagrandalivigno.com
* Centro Italiano Sleddog, Husky Village: 0039 0342 927 072; huskyvillage.it