Rural communities are facing a prolonged blackout after high winds and heavy snow brought down power lines and cut off supply routes.
The isle of Arran and parts of the south-west mainland of Scotland were particularly badly hit.
Power companies are working with councils to send generators to affected areas while engineers try to clear routes and restore energy.
A spokesman for Scottish Hydro said engineers are working to get people back on the grid on Saturday, but that access is not possible to all parts of Arran.
"Mobile generators are on the island and more are en route but access is proving difficult," he said. "We're trying everything we can to get people back on today but we can't give an indication of when everyone will have their power restored."
Whiting Bay Hall and Auchrannie Spa and Country House, in Brodick, are open for residents with power, heat and refreshments, North Ayrshire Council advised.
Lamlash fire station is open all day with power available through a local generator.
Other areas badly affected by power cuts are around Campbelltown and on the islands of Islay, Jura and parts of Bute, according to Argyll and Bute Council.
A spokesman for energy provider ScottishPower said: "We have approximately 6,000 homes still off supply in the south-west, predominantly in the Wigtownshire area.
Driving conditions were also widely affected by snow and high winds, mainly in the south-west and north-east.