The heaviest snow was falling on Pennsylvania, New York and New England, and winter storm warnings continued over a majority of the U.S. Northeast, the National Weather Service said.
The massive storm system touched off tornadoes in the South and produced snow in Texas before barreling down on the densely populated Northeast.
The service forecast 12 to 18 inches (30.5 to 46 cm) of snow for northern New England after the storm moved northeast out of the lower Great Lakes, where it left more than a foot (30.5 cm) of snow on parts of Michigan.
The storm front was accompanied by freezing rain and sleet, creating hazards on the highways and at airports.
A Southwest Airlines jet skidded off the runway at Long Island MacArthur Airport, about 50 miles (80 km) east of New York City, as it taxied for takeoff, Suffolk County police said.
None of the 134 people aboard Tampa-bound flight No. 4695 was injured, police said.
"It's been undetermined at this time if weather was a factor," a police spokeswoman said.
Snow was due to fall in northern New York, Vermont and New Hampshire at up to 2 inches (5 cm) an hour, with winds gusting to 30 miles per hour (48 km per hour), the weather agency said.
So far, 457 U.S. airline flights scheduled for Thursday had been canceled, according to FlightAware.com, a website that tracks flights.
American Airlines had the most canceled at 55. A total of about 1,500 U.S. flights were canceled on Wednesday.
New York state activated its Emergency Operations Center late on Wednesday to deal with the first major storm of the season.
Governor Andrew Cuomo warned the heads of seven utilities they would be held accountable for their performances. Utilities near New York City were criticized for lingering outages after Superstorm Sandy devastated the region in October.
New York state has seen little snow during autumn and winter. Buffalo, New York, was 23 inches (58 cm) below normal for the season before the storm, said Bill Hibbert, a National Weather Service meteorologist.
"We're short and even this big snow isn't going to make it up for us," he said.
The storm dumped record snow in north Texas and Arkansas before it swept through the U.S. South on Christmas Day and then veered north.
The system spawned tornadoes and left almost 200,000 people in Arkansas and Alabama without power on Wednesday.
At least five people were killed in road accidents related to the bad weather, police said.