Road conditions appeared to be getting bad in parts of the county, according to Dane County Sheriff's Office spokeswoman Elise Schaffer.
"The worst seems to be on Scherbel Road in the town of Berry," Schaffer said. "It was real slick on a hill, and vehicles were sliding off the road."
Other slide-offs have been reported in the towns of Vermont and Westport.
Five school districts were closing early or were already closed.
Albany schools closed at noon, Argyle and Darlington schools were closing as 12:30 p.m., Black Hawk schools were closed, and no afternoon pre-kindergarten classes were being held in Mineral Point.
The state highway road condition report showed slippery stretches on major highways in most parts of the state as of 10 a.m.
In southern Wisconsin, U.S. 151 from Madison to Dubuque, U.S. 14 from Lone Rock to Coon Valley, Wisconsin 13 from Wisconsin Dells to Westboro, I-90/94 from Camp Douglas to Tomah, and I-39 from Portage to Wausau were considered snow-covered and slippery.
Travel conditions were also getting tough in central Wisconsin, with numerous accidents and slide-offs reported because of the snow.
The Wisconsin statewide traffic operations center issued a traffic advisory because of slippery conditions throughout central Wisconsin, advising motorists to slow down and expect delays.
The National Weather Service issued a winter weather advisory in effect until 3 p.m. Wednesday, with snow starting in the western part of the state and moving east. The snow is expected to taper off by mid-afternoon.
Wisconsin State Patrol Sgt. Gary Bauer told The Capital Times there were some crashes and slide-offs in Sauk and Columbia counties.
"People should be aware of changing road conditions," Bauer said. "Lower your speed and keep a good distance between yourself and the vehicle ahead of you."
Madison Streets Superintendent Al Schumacher said 30 salters and sanders were out on city streets, mostly working on the main arterials and bus routes.
"The main streets are staying clear but some of the secondary streets and residential streets are getting a little snow buildup," Schumacher said.
No snow emergency had been declared, but one could be issued later Wednesday. The city would need to call one by 9 p.m., but Schumacher said it most likely would be earlier in the day if conditions warrant.
"Stay tuned for further updates," Schumacher said. "If I had to guess, we'd probably call one by 3 p.m. if we were going to call one."
Residents can go to the city's winter Web site at http://www.ci.madison.wi.us/residents/winter/ to find out if a snow emergency is declared and also to sign up for e-mail or text message notification.
County crews were out in force clearing major highways and county roads, said maintenance superintendent Dan Behrend.
"The pavement was pretty warm so the roads aren't too bad," Behrend said. "People should use caution when driving."
He said roads in the western part of the county are getting some buildup but the county drivers haven't seen any incidents yet of cars off the highway.
The afternoon drive time will be hampered by blowing and drifting snow caused by stiff northwest winds, with travel conditions expected to deteriorate in the late afternoon, the Weather Service said.
"Be prepared for snow-covered roads and limited visibility, and use caution while driving," the weather advisory said.
Weather Central meteorologist Brian Olson said Madison should end up with 2-4 inches of snow, with greater accumulations to the north and southeast.
The snow is accompanying a cold front that will drop temperatures to the low teens Wednesday night and a high of 20 on Thursday. The thermometer could dip to eight degrees Thursday night, with wind chills dropping down to five degrees below zero.
After a partly sunny Friday with a high of 22, clouds will roll in, and more snow is expected Friday night into Saturday, but only several inches are forecast. Sunday should be sunny with a high of 24, but snow could come back to south central Wisconsin on Monday and Tuesday.
Tuesday's high in Madison was 33, two degrees below normal and 29 degrees below the record of 62 for Dec. 2 set in 1982.