"Over 20 million people are under winter weather alerts, over 8 million people are under a flash flood threat, and over 9 million people are under wind advisories," CNN meteorologist Haley Brink said Sunday.
More than 12 inches of snow will fall Sunday in the southern and central Appalachians, the National Weather Service said.
WATCH: Grinch plows snow in Boone, N.C.
Snowfall could total 12 to 20 inches over the Appalachians and into the Carolinas by Monday, when the storm is expected to move off the coast, the NWS said.
"Snowfall amounts in some locations will likely exceed a foot and result in several days of difficult or impossible travel, extended power outages, and downed trees," the agency said.
The storm already has knocked out power for more than 546,000 customers in the Southeast.
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The bulk of the outages are in North Carolina, where 244,807 customers are in the dark. In South Carolina, more than 225,600 customers have lost power. And Alabama, Tennessee and Georgia each had about 20,000 and 30,000 customers are out of electricity.
Those hoping to escape the storm may be out of luck. More than 1,100 Sunday flights into and out of North Carolina's Charlotte Douglas International Airport have been canceled, according to flight tracking website FlightAware.
More than half the Sunday flights at Raleigh-Durham International Airport and Piedmont Triad International Airport have also been called off.
North Carolina has 500 car wrecks in 11 hours
In Durham County, residents typically get about 6 inches of snow over an entire year. But on Sunday morning, they woke up to see 6 inches of snow on the ground.
"The roads in Durham are treacherous and not safe for driving," the Durham County Sheriff's Office tweeted.
Authorities responded to more than 500 car crashes between midnight and 11 a.m. Sunday, North Carolina Gov. Roy Cooper said. One tractor trailer ran off the road and into a river.
"We've seen too many collisions," Cooper said. "From Charlotte across central North Carolina, the biggest concern now is ice making roads even more dangerous."
Even before the storm hit, Cooper declared a statewide emergency. Grocery store shelves were cleared of bread, milk and other staples.
Cooper asked residents to check on vulnerable loved ones and the elderly, if possible. He said 11 emergency shelters have opened across the state.
North Carolina Highway Patrol said anyone who must drive should leave twice as much following space behind the next car, in case that vehicle loses control.
'Ice is becoming a big problem' in South Carolina
In South Carolina, a state known for palmettos rather than freezing rain, ice-covered roads are making driving conditions perilous.
"Ice is becoming a big problem. Please stay off the roads," Greenville County Emergency Management pleaded.
The local National Weather Service office had to adjust its forecast map Sunday after it became clear more ice was expected near Interstate 85.
"We have increased our ice (accumulation) forecast quite a bit along the I-85 corridor," the NWS Greenville-Spartanburg office said.
And with ice and heavy snow come power outages.
As of 4:30 a.m. Sunday, 2.5 inches of snow had fallen in the Greenville-Spartanburg area.. Half an hour later, the county's emergency management office said 14,189 customers had lost power.
The storm left a trail of misery in Texas
Before striking the Southeast, this moisture-heavy storm walloped Texas flash flooding along the southern edge of the state and snow and ice in the north.
As the moisture moved east, it collided with a high-pressure system over the Ohio Valley that is funneling cold air into the region.
In Lubbock, Texas Tech University rescheduled all Saturday final exams for Sunday.
Parts of Lubbock were buried under 10 inches of snow -- 2 inches more than the city usually gets in a whole year.
"They crushed their yearly average in 24 hours," CNN meteorologist Ivan Cabrera said.
More flight cancellations to come
Grounded airline passengers might remain stuck Monday as more flights get canceled.
The Charlotte airport said it expects cancellations through Monday morning, mostly involving small, regional planes.
American Airlines, whose second-largest hub is in Charlotte, has canceled 1,100 flights for Sunday. It's not clear when those passengers will be able to get on board, since another 320 flights scheduled for Monday already have been nixed.
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