A less serious class-one alert was issued for Värmland, Dalarna, Örebro, Västmanland, the rest of Uppsala and the northern Stockholm coast – an area that includes Norrtälje municipality, where more than 6,000 households are still without power and running water after Storm Alfrida hit almost a week ago.
National weather agency SMHI warned that some 5-15 centimetres of snow could fall, with wind causing snow drifts.
In the class-two areas it predicted 10-20 centimetres of snow between Tuesday morning and Wednesday night, and up to 25 centimetres of fresh snow in some local areas.
In Dalarna a dairy truck went off the road early on Tuesday morning, but no injuries were reported. Police urged drivers to take it easy and keep their distance on the road.
Storm Alfrida wiped out the electricity grid in some places in Stockholm and Uppsala counties when it hit Sweden's east coast between Tuesday and Wednesday last week.
Power companies are working to restore electricity to households in the region, but have said it is going to take some time in places where the grid has to be rebuilt from scratch.
In Norrtälje, many fire stations, sports halls and schools are keeping their doors open for residents, offering places to eat, shower, collect fresh drinking water and sleep.
The municipality has asked the Swedish Armed Forces for help in the form of tracked vehicles, due to emergency services' concerns that more trees could fall under heavy snowfall accompanied with wind.
“If there's so much snowfall that the roads aren't accessible, or if a lot of trees fall and we can't clear the roads when we need to get to someone who needs care or rescue, then we need tracked vehicles,” explained Jacob Öhrn from Norrtälje's emergency services, speaking to the TT newswire.