In the French Alps, a slight break in the weather meant rescuers could begin looking for a British skier who went missing on Sunday in the resort of Tignes, police said.
In the southern Swiss canton of Valais, snow has blocked transportation links by road and rail to Zermatt, station head Janine Imesch told AFP.
There are currently "around 13,000 tourists at Zermatt" where the main access road has been closed since early Monday, while the train was halted Monday evening, she said.
Zermatt is home to some 5,500 inhabitants and has the capacity to accommodate 13,400 tourists spread across hotels and rental apartments.
But the stranded tourists will not be able to take advantage of the abundant snow for the time being due to an avalanche risk, which is at its highest level.
"It is not possible to do downhill or cross country (skiing), but that's ok. It's a bit romantic," Imesch said, adding that "there is no panic."
The heavy snowfall also caused power outages in some areas of the canton, and a number of other villages were also cut off, with the Simplon region of Valais hit by two metres (6.6 feet) of snow in a 24-hour period, the ATS news agency reported.
Mud and rockslides, as well as flooding, closed a number of roads across Valais. At lower altitudes, heavy rains forced the evacuation of around 20 people from Eyholz village and with the nearby hamlet of Mottec also emptied as a precaution, Swiss media reports said.
Further to the north, snow and high winds prompted the cancellation of Tuesday's first men's World Cup downhill training run in Wengen, in the canton of Bern, organisers said.
Although the piste itself was unaffected, overnight winds of up to 200 kilometres per hour (125 miles per hour) caused significant damage to infrastructure on the course, notably at the finish where tents and the stands were hit.
'Once every 30 years'
In the Italian Alpine resort of Sestrieres, where more than two metres of snow fell in 48 hours, an avalanche struck a five-storey building late on Monday, sending a mass of snow and broken branches into its corridors and even into several apartments, media reports said.
But the 29 people staying there managed to escape the building unharmed through the garage.
Heavy snowfall has blocked access to some Italian resorts and villages, among them Cervinia in the Valle d’Aosta region.
But with the school holidays now over, the number of tourists and residents cut off by the snowfall was around 5,000, sharply down on the 11,000 people in the area last week, Italian media reports said.
On the French side, where Meteo France said Tuesday the avalanche threat has diminished, rescuers were able to start looking for a British skier missing for the past two days, with a helicopter searching the area where a signal from his mobile phone was last picked up.
The 39-year-old went missing in the resort of Tignes on Sunday after saying he wanted to complete "one last run", police said.
Parts of the Savoie area of the Alps have seen up to 1.8 metres (six feet) of snow in just 36 hours in what French forecasters described as snowfall only seen "once in every 30 years."
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