"Blizzard and winter storm warnings are in effect for the northern Texas panhandle, the Oklahoma panhandle and much of central and western Kansas," said the National Weather Service, warning that travel in the region would be "quite treacherous."
At least six deaths had been reported by Tuesday morning, according to the Associated Press.
Four people were killed when their vehicle hit a pickup truck in eastern New Mexico, while a prison guard and inmate died in a crash in eastern Colorado.
Many more motorists were left stranded. Nearly 100 rescue calls were taken from drivers in northern Texas, where the blizzard forced authorities to close part of the Interstate 40, the AP said. Sections of New Mexico's I-25 and the I-70 in Kansas were also shut. Hotels were said to be filling up along closed highways.
The storm hit the region Monday, covering roads with ice and severely reducing visibility. The heaviest snowfall was over eastern Colorado and western Kansas, according to the NWS. Some areas had north winds of up to 40 mph with gusts to 50 mph, creating blizzard conditions.
The worst of the snow was thought to be over by Tuesday morning, the forecasters said, though strong winds will continue to shift the snow drifts that built up during the night, and blizzard conditions are expected.
"Travel through the region will likely be extremely difficult, if not impossible, during the day on Tuesday," the service warned.