The system that carried the snow to Minnesota, Wisconsin and Illinois is the same one that dumped more than a foot of snow across Kansas and Oklahoma Thursday and closed schools, highways, even state legislatures in some states, NBC News reported.
The storm system spanned 20 states, CNN said.
"I do want to urge everybody in the state: If you don't have to travel, don't," Brownback said. "Get out a board game, play with the kids, drink a cup of coffee."
As the system trekked across the central United States, accidents were reported, with at least one fatality -- an Oklahoma teenager was killed Wednesday in a truck on a slushy road.
Hundreds of flights were delayed or canceled at airports in the system's path Thursday, and more delays and cancellations were expected Friday.
Minnesota's twin cities of Minneapolis and St. Paul and surrounding suburbs could get up to 6 inches of snow by the time the system clears.
If 4.8 inches of snow falls on the Twin Cities, this would become one of the 10 snowiest Februarys on record in the metro area, coming off a winter that started with little snow and a summer-fall drought, the Minneapolis Star Tribune reported.
Chicago and surrounding areas got about 3 inches of snow and that was expected to turn to freezing drizzle Friday, the Chicago Tribune reported.
The city of Chicago sent 284 plows to clear main thoroughfares, the streets and sanitation department said.
The weather caused between 20 and 30 spinouts on highways across the city and suburbs, state police said, calling the conditions "horrible."
By the time the system moved out Thursday, 14 inches of snow had fallen in Wichita, Kan., the second-largest on record and the most the city experienced in half a century, NBC News said.
Sleet and freezing rain were forecast for Friday in southern and central Ohio, West Virginia, western Virginia, parts of central and western Pennsylvania and possibly northern North Carolina.
The same weather system could dump snow on New England for the third straight weekend, AccuWeather.com said.
Boston, which has received 32 inches of snow so far this month, could break a February snowfall record with this storm, meteorologists said. The February record is 41.6 inches.