Some properties in the north of Scotland may not be reconnected to the electricity grid until Friday.
About 14,000 homes are still without power after Storm Gerrit brought blizzards and flooding to Scotland.
Properties have been flooded in Cupar, Fife, while drivers were stranded by snow on the A9 in the Higlands on Wednesday evening.
The road was shut at Scrabster due to a landslide though one lane has reopened.
Power company SSEN said customers in the north east and Shetland had been worse affected, with some power outages likely to continue into Friday.
Elsewhere in the UK, a hundred homes were damaged after a “localised tornado” tore through the Tameside area of Greater Manchester.
Rail services north of Perth and Dundee remained shut down on Thursday morning and key routes between Aberdeen, Dundee and Inverness were closed.
There was also flooding in the Whitesands area of Dumfries and on the A96 at Huntly, while trees have fallen across the A82 south of Invergarry.
Graeme Keddie, SSEN’s director of corporate affairs, said that by 07:30 on Thursday about 14,000 homes were still without power after 31,000 had been reconnected. Most of those affected are in the north east or Shetland, he told BBC Radio’s Good Morning Scotland.
He apologised to those without power, adding: “We’re doing all that we can to restore supplies as soon as possible.”
Mr Keddie said engineers had made “really good progress” despite “extremely tough conditions”.
Image source, Bear Scotland
He said customers should monitor the SSEN Power Track website and urged those who had not had a restoration time by mid-morning to get in touch using the free-phone 105 number.
Mr Keddie insisted the firm had made “big improvements” on its main network and customer communications after thousands were left without power for a week following Storm Arwen in 2021.
The Met Office issued a yellow weather warning for much of Scotland on Wednesday.
A yellow warning covering Shetland extended until 06:00 on Thursday, with Lerwick registering its strongest wind gust in seven years at 83mph.
A major incident was declared by Highland Council as the A9 was shut for hours due to heavy snow, leaving drivers trapped in their vehicles near the Pass of Drumtocher.
Caledonian Sleeper services, to and from Aberdeen, Inverness and Fort William were cancelled on Wednesday night while the British Transport Police was called out to reports that a train had been struck by a tree near Broughty Ferry station.
Pictures showed extensive damage to the driver’s cab.
Stein Connelly, head of transport resilience at Transport Scotland, said: “The weather has improved and the Met Office warnings have ended, but people may still encounter difficult driving conditions due to surface water and flooding.
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“We continue to ask people to plan ahead, to drive appropriately and to take care out on the road network.”
CalMac said some ferry services on Thursday were at risk of disruption or cancellation at short notice.
The operator said the latest information on delays and disruption to other routes was available on the CalMac website.
NorthLink services across the Pentland Firth to Orkney were also at risk of disruption.
First Minister Humza Yousaf said the Scottish government’s resilience operation had been activated on Wednesday evening.