Careering out of thick cloud came a large husky, tugging a skier behind him. The man flew over a bump and arced through the air, skis inches from my chest, then pelted at breakneck speed down the slopes. As the Slovak saying has it, he was “skiing like a Hungarian”.

My Slovak hosts here in the ski resort of Tatranská Lomnica were dubious when I told them what had happened. “This, no, I never saw,” said hotel manager Michal. But he had seen bears passing outside his lobby, he said, and 30 wild boar on the roadside one night.

This wild landscape was shrouded in cloud during my visit, so I had to take much of what they told me on trust. The panaroma from the 2,364-metre Lomnický peak, a cablecar ride from the top of the ski area, is apparently dramatic on clear days. Despite the heights, the skiing here in the High Tatras (including its Starý Smokovec and Štrbské Pleso resorts) is limited, and suitable mostly for beginners and families.

But if that’s for you, organising a weekend ski trip here is easy, thanks to a new Wizz Air flight from Luton to Poprad, a 10-minute taxi ride from these slopes. And more experienced skiers can drive 40 minutes further to the Low Tatras, home to Slovakia’s biggest and best ski resort, Jasna. With 29 pistes, Jasna is smaller than many Alpine resorts, but has long runs and decent off-piste potential.

Any outdated preconceptions of old eastern European infrastructure are soon dispelled: the lifts are modern, with heated seats and bubble covers.

Jasna has pistes up to about 2,000 metres. Photograph: Gwyn Topham

Being below 2,000 metres, Jasna relies on artificial snow to keep all the pistes open, and during my visit, scant January falls meant no real off-piste. But with decent snow, the designated freeride zones on the rock-free southern slopes of 2,024-metre Chopok form a broad, accessible bowl.

I encountered two rare British visitors, Katie and Mark from London, who had skied the fresh stuff under blue skies here. They were smitten by Jasna, even though their usual choice is Jackson Hole, one of America’s top resorts. They appreciated the lower costs here: a free bus serving the lifts runs along the valley road to Liptovský Mikulas, along which B&Bs can cost as little as €25 a night (visitliptov.sk). And a beer costs a magical €0.70 at the bar in Demanova village – nicknamed Club Tropicana by British visitors (“because drinks are almost free”, said Mark).

Eating on the slopes is also good value: at the pricier end, Von Roll, a converted lift station, serves mains including homemade pasta from about €10. Beside the blue run, a Slovak koliba (mountain hut) cooks the halusky (the national dish of sheep-cheese gnocchi with lardons) for €5 a portion. Ski hire and lift passes each cost around €20 a dayeach for longer stays), a hefty sum by Slovakians standards - many choose instead to hike up the pistes on touring skis. There appears to be an appetite for more strenuous physical activity here: the Spartan race, a kind of cross-country mountain slog dotted with barbed wire obstacles to climb over or crawl under, was having its first snowbound outing here, with the locals emerging victorious from an international field

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Jasna has some 46km of piste

There is an abundance of hotel spas and waterparks. Alarming posters for Tatralandia, linked on the free ski-aqua bus from Jasna, shows a scantily clad woman wearing a python, but it is very much a family place. Saunas and spa rooms give way to a wealth of pools and startlingly rapid slides.

The High Tatras have a gentler side, with lovely Austro-Hungarian empire establishments that could double as the Grand Budapest Hotel – the sort of place where Ralph Fiennes’ concierge entertains wealthy octogenarians: all wallpaper, chandeliers and reproduced artworks In 2008, Prince Philip stayed at the Grandhotel in Stary Smokovec; Harold Wilson, who has a lounge named after him, presumably stayed, too. The Wilson bar is upstaged by the hotel’s Castro cafe, though: pictures showing Fidel stripped to the waist were taken on a 1972 visit, when he hunted chamois before an epic table tennis duel against the hotel’s boiler man.

It’s a history that smacks of surreal Wes Anderson fantasy, were it not for the photographic evidence.

• Accommodation was provided by Tatry Mountain Resorts , with nights at Jasna’s Ostredok hotel (doubles from €105 in ski season, ostredok.sk) and the Grandhotel in Stary Smokovec (doubles from €80, grandhotel.sk). Flights were provided by WizzAir, which flies from Luton to Poprad-Tatry from £47 return