"The objective is to keep everyone safe," said David Ponson, ski chief in the Alpine Savoie region, as many pistes were shut for a second day.
Eleanor, the fourth winter storm to hit Europe since December, swept into the continent on Wednesday after battering Britain and Ireland.
It has killed at least six people, including a 21-year-old skiier hit by a falling tree in France and a couple in their 60s swept away on Spain's northern Basque coast by a huge wave.
A 45-year-old woman and her 11-year-old daughter died after being hit by an avalanche while skiing in Vinschgau, South Tyrol in Italy.
On Thursday, firefighters said a woman in her 90s died of a heart attack in Crets-en-Belledonne in the French Alps after floods sent a torrent of mud and water into her home.
And a volunteer rescuer was reported missing after rushing to help when a car plunged into an overflowing river in the Alpine village of Le Moutaret.
At Lenk in central Switzerland, eight people were hurt when a violent gust of wind overturned a railway carriage.
The worst of the storm appeared to have passed by Thursday, though much of eastern France was still on "orange" alert for heavy winds, floods and avalanches.
"The intensity of the rain and melting snow bring a risk of floods via overflowing streams and mudslides," warned forecaster Cecile Coleou.
About 29,000 French homes remained without power, a third of them in Corsica.