The Savoie department prefecture said 3,500 motorists spent the night in emergency shelters after the snow made the roads impassable.
A further 500 holiday-makers who landed at the airport in the city of Chambery also had to sleep in shelters.
Three people die in avalanches in Swiss Alps
The avalanche alert level in Savoie was at four on a scale of five, the national weather service said.
The mountain rescue service said a 22-year-old man died when an avalanche swept him away as he skied off-piste on Saturday in Val d'Isere, a resort popular with foreign visitors.
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