"We are currently investigating ten breaks" says Magnus Kryssare at Vattenfall. He says to news agency TT that Vattenfall does not know when the electricity will be back again for the 13,596 customers affected, but that it will hopefully be soon.
In the early morning 4,289 customers of power company Eon were also without power, but the company now says the electricity is back on. And the other big power company, Fortum, has 1,000 affected by power cuts.
Stockholm busses are suffering delays, and in parts of greater Stockholm services have been cancelled, or forced to use detours, due to the slippery roads.
The northern Stockholm train line Roslagsbanan is also currently replaced by busses along certain stretches that have been hit by power cuts, and the eastern Stockholm Saltsjöbanan train service has been completely replaced by busses, due to a tree falling on one of the overhead power lines.
So is this thick springtime snow very unusual? Therese Fougman at the Swedish Meteorological Institute (SMHI) says no.
"In the middle of April just about anything can happen. Things can go a bit back, and see a bit of snowfall."
But it will be rain falling over east-central Sweden later in the day. The snow will probably melt - bu don't hold your breath waiting for the warm sun to come back.
"It looks a bit feeble", says Therese Fougman.