The north of the country bore the brunt of the bad weather and yellow ''be aware'' warnings for high winds remain in place for the Highlands and Islands, Orkney and Shetland.
The highest recorded gusts last night were 82mph in Peterhead, 77mph in Inverbervie and 75mph on South Uist. The rest of the country was buffeted by speeds of between 50-60mph, causing Christmas attractions in Edinburgh to temporarily close.
Scottish Hydro said 3,500 homes lost electricity last night with just under 1,800 still cut off from the grid this morning. Around 1000 had been reconnected by 5pm.
Elgin, Aberdeenshire and communities in the Northern and Western Isles have been worst affected by the power cut.
A spokesman said: "Engineers have been working to repair the faults since six this morning and we expect to have everything repaired today, some affected areas are in very remote locations like Yell but we are working to get staff to sort them as well."
Christmas travel plans were disrupted for hundreds of people yesterday, with ferries and flights cancelled, particularly to the Western Isles.
In a first for Christmas Day, CalMac is running special sailings to North Uist and Harris, weather permitting.
Many flood warnings remain in place, particularly for Tayside where river levels have been high.
Ben Windsor, a forecaster with MeteoGroup, said: "The winds will be easing off through the day but here will still be gusts of around 45mph in the Hebrides and around 35mph on the west coast.
"The north west looks like it will be worst affected again with rain while most of the mainland will be relatively dry. There will even be some bright spells, particularly in Aberdeen and in the south of the country with Glasgow and Edinburgh just on the edge of the clouds.
"There was some snow on higher ground yesterday but it's only really a white Christmas on the mountain tops where the rain begins to turn to snow at 300 metres and above."
In yesterday's high winds a portion of the roof at Thurso High School in Caithness was blown off, damaging two vehicles. Part of an empty building in Linkwood Road, Elgin, was also damaged, with three families evacuated from nearby houses as part of the structure collapsed on to the road.
At the other end of the country, fallen trees and debris caused problems on some roads in the Borders with a mudslide temporarily closing the A7.