Households on the mainland or on islands with bridges or ferry routes to the mainland should get power back on Thursday, January 10th, at the latest, according to a statement from Vattenfall.
But customers on some islands may have to wait for another two weeks, until January 25th.
There was further snowfall on Tuesday, but not in such high quantities as forecast.
National weather agency SMHI issued a class-two warning for heavy snow in Gävleborg and Uppsala. The heaviest snowfall was expected in Gästrikland and along the northern part of the Uppland coast, but SMHI revised its forecast down from 25 centimetres of fresh snow to 20.
“It's not snowing with the intensity we had anticipated, quite simply,” SMHI meteorologist Henrik Reimer told TT.
However, the weather warnings remained in place and the blizzards were also impacting traffic. The Swedish Transport Administration warned of a difficult transport situation around Gävle due to the snow, while in other areas, including western Sörmland, the roads were particularly slippery.
Meanwhile, SMHI has warned that there may be storm-level winds across Norrland and especially in coastal areas on Friday.