The Nebraska Department of Roads reported no highway closures Tuesday but warned of icy conditions in southwest Nebraska.
"There was ice underneath the snow," Kunnemann said Tuesday. "The roads were bad. There were some wrecks ... cars went off the road because the snowplows hadn't got out yet."
Some Nebraska school openings were delayed. Several southern Minnesota school districts started classes two hours late and a few closed for the day because of the weather.
The weather service said up to 4 inches of snow was possible across southern Minnesota into Wisconsin.
In western South Dakota, utility crews were still working to restore electrical service knocked out by a blizzard last week. An estimated 1,800 customers of six electric cooperatives have been without power since that storm.
The South Dakota National Guard has sent an 11-man team to help open roads for the electrical work crews. Deep snow driven into 7-foot drifts has slowed the repairs, and Ken Wetz, manager of Butte Electric Cooperative, said about 3 inches of ice still covers some downed wires.