Fewer than 100 homes remain without power after thousands were cut off at the height of the storm.
Met Office yellow ''be aware'' warnings for high winds in the Highlands and Islands, Orkney and Shetland are no longer in force.
A total of 15 flood warnings are still in place after rain showers swept across the country.
The majority of these are in Tayside where river levels are said to be high.
Northern areas bore the brunt of the bad weather yesterday with the highest gusts recorded at Peterhead (82 mph), Inverbervie (77 mph) and South Uist (75 mph).
The rest of the country was buffeted by wind speeds of between 50-60mph, causing Christmas attractions in Edinburgh to temporarily close.
Scottish Hydro said 3,500 homes lost electricity and just under 1,800 were still cut off from the grid this morning.
Engineers are continuing to repair faults and it is hoped the remaining 100 properties will be reconnected by around 8.30pm.
The worst affected areas are Aboyne and Banchory in Aberdeenshire and Elgin and Lhanbryde in Moray.
Ben Windsor, a forecaster with MeteoGroup, said: ''The winds will be easing off through the day but there 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.''
Christmas travel plans were disrupted for hundreds of people yesterday, with ferries and flights cancelled, particularly to the Western Isles.
High winds blew off a portion of the roof at Thurso High School in Caithness, 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.