(CNN) -- People across much of the United States braced for more havoc Wednesday from a strong winter storm that was bringing blizzard conditions to some areas and rain and high winds to others.
The National Weather Service issued a blizzard warning for parts of several Midwestern states for Wednesday, saying that places such as North Dakota and Minnesota could get dangerous wind chill readings of 25 to 35 degrees below zero.
By 4 a.m. ET Wednesday, Madison, Wisconsin, had received 15 inches of snow, prompting the University of Wisconsin to cancel classes, according to CNN affiliate WISC-TV. Schools were closed across Iowa and Wisconsin and parts of Minnesota.
"I wouldn't advise anyone being out in this stuff now," truck driver Bill Hyde told CNN affiliate WISN-TV.
The storm prodded Nicole Stec of Janesville, Wisconsin, to finally buy those new tires her car had been needing.
"I'm a procrastinator, so I put it off for a while. But now it's time because there's snow on the ground," Stec told WISC-TV at a Janesville tire shop. "It's my Christmas present from Santa, apparently."
Des Moines, Iowa, had received more than a foot of snow, with more to come, and Freeport, Illinois, had 11 inches.
Snow and sleet fell on Chicago, Illinois, canceling more than 325 flights Tuesday at O'Hare International Airport, according to a spokesman for Chicago's Department of Aviation. No delays were reported at O'Hare early Wednesday.
New England also was expected to get dangerously low temperatures and heavy snow in some parts Wednesday. Areas in Maine were expected to get as much as 10 inches, the weather service said.
Connecticut's Department of Transportation deployed all of its 632 trucks to clear roads of snow that prompted numerous school closings Wednesday morning, CNN affiliate WFSB-TV reported.
The storm left its mark on the West on Monday and Tuesday.
Alpine Meadows, California, near Lake Tahoe received 42 inches of snow before the storm moved out of the region Tuesday afternoon. Pagosa Springs, Colorado, received 33 inches, and Flagstaff, Arizona, got 30, with similar amounts throughout the Rockies.
The storm brought high winds to the Southwest. Guadalupe Bowl, Texas, recorded a wind gust of 105 mph, and gusts of 78 mph were observed in Chino Valley, Arizona, and Maljamar, New Mexico.
Andres Rodriguez of El Paso, Texas, told CNN affiliate KFOX-TV that he went to check on his mother in Montana Vista after he heard that flying debris from a mobile home had just missed hitting her.
"She was walking by here and she almost got hit by a wall because of the wind. Everything is falling apart," Rodriguez said.
Heavy rain fell across the South, as New Iberia, Louisiana, reported 6.7 inches.
Floodwater damaged a dozen homes in St. John the Baptist Parish, Louisiana, CNN affiliate WDSU-TV reported.
"It was terrible. When I looked out the window this morning, I seen my car was underneath the water and I was afraid," said Anita Jones of Mount Airy.
Heavy thunderstorms downed trees and power lines and overturned a mobile home in Greenwood County, South Carolina, CNN affiliate WYFF-TV reported. -- CNN's Larry Frum and Jim Kavanagh contributed to this report.