Emergency crews were having trouble reaching drivers who were caught on the roads, Texas Department of Public Safety Trooper Gabriel Medrano said. Cars were in ditches, he said, because drivers couldn't tell where road ended and ditch began.
National Guard units were being sent to help stranded motorists, the Texas DOT said.
CNN iReporter Jason Boyett in Amarillo posted a video showing near-whiteout conditions at 7:40 a.m., and followed that with another showing a drift nearly 3 feet high outside his front door.
"We get high winds and we get big snowstorms, but they're not often combined," Boyett said.
Whiteouts were also reported in Oklahoma, where as of 10 a.m. Central time, the state had closed all highways in six counties -- Ellis, Harper, Woodward, Beaver, Texas and Cimarron -- until further notice.
"Roadways and ditches are snow packed with no visibility and are very slick and hazardous. All travel is discouraged," the Oklahoma Department of Transportation said. As much as 16 inches of snow could fall in western areas of the state, the weather service said.
Oklahoma Lt. Gov. Todd Lamb declared a state of emergency for 56 of Oklahoma's 77 counties.
Visibility was low in Fairview, Oklahoma, midway between the Panhandle and Oklahoma City, said CNN iReporter Brandi Whitacre.
"Right now it is snowing so heavily I can barely see down our driveway, which is 100 yards or so. It is coming down," said Whitacre, who added that'd she'd lost satellite TV service and was experiencing intermittent power outages.
The blizzard is the second major winter storm to hammer the region in a week.
The number of people under blizzard and winter storm warnings, watches and advisories totaled 35 million, according to CNN's weather unit.
Wichita schools were closed for the third straight school day as the new storm roared in on the heels of one that dumped up to 22 inches of snow on some areas late last week.
Kansas' governor on Sunday extended a state of emergency declaration to include the new storm.
Gov. Sam Brownback said Monday that one person had been killed in a single car accident in Sherman County. Officials blamed the fatal wreck on icy roads.
The Kansas Department of Transportation reported that many highways in the central part of the state, including Interstate 70, were completely covered by snow and ice on Monday morning.
All flights in and out of Rick Husband Amarillo International Airport in Texas were canceled until noon on Monday.
Preston Smith International Airport in Lubbock was also closed, CNN affiliate KCBD reported, and Texas Tech University in Lubbock shut down on Monday because of the storm.
While millions will see snow -- including Chicago, where 3 to 7 inches of snow and sleet are expected by Wednesday morning -- rain may rule for the next few days in parts of the Southeast.
In Mobile, Alabama, on the Gulf Coast, residents prepared for the possibility of heavy rain and wind gusts as strong as 30 mph by Monday night.
The rain is part of a band affecting several Southern states where tornado watches were in also effect Monday night.