A strong winter storm that coated highways in the Carolinas and Georgia with ice and knocked out power to nearly 200,000 customers was headed on Sunday to the Northeast, where it was expected to leave about a foot of snow in some places.

In the South, where some governors declared states of emergency, areas such as central Mississippi and central North Carolina had already received more than nine inches of snow, while portions of central South Carolina had up to a half-inch of ice, the National Weather Service said.

“This storm is going to be pretty significant in terms of generating travel impacts, outages and things of that nature,” said Rich Otto, a meteorologist with the Weather Service.

Officials in the Northeast urged people to stay off the roads on Sunday night, warning that the storm was expected to bring up to a foot of snow in some parts, including the Appalachians and upstate New York, and nearly two feet in northwestern Pennsylvania.

Meteorologists said that in parts of the Northeast, the snow could fall at a rate of three inches an hour on Sunday evening.

“Overnight is going to be very unpredictable,” said Gov. Kathy Hochul of New York. “And with the darkness and ice on the roads and high winds, this could be a very dangerous situation.”

Gov. Philip D. Murphy of New Jersey said at a news conference that “things are going to be wet, windy and messy” as the storm barreled through the state on Sunday, with wind gusts of up to 50 miles an hour battering the state into Monday morning.

By early Sunday afternoon, the storm had already had an impact in several Southern states.

In Georgia, about 42,000 customers were without power on Sunday evening, according to PowerOutage.us, which aggregates data from utilities across the United States. South Carolina and North Carolina each had more than 65,000 customers without power.

More than a quarter-inch of ice accumulated in parts of the Piedmont regions of North and South Carolina on Sunday, said Frank Pereira, a meteorologist with the National Weather Service.

Gov. Roy Cooper of North Carolina warned residents at a news conference on Sunday to stay off the roads because parts of the state had received up to a foot of snow.

“For today, the best way to avoid a car accident or getting stranded is to stay put,” he said.

As of Sunday morning, there were already 200 reports of crashes as a result of the storm, said Col. Freddy Johnson Jr., the commander of the State Highway Patrol.

“Travel is treacherous across much of our state,” Colonel Johnson said.

The North Carolina officials said on Twitter that “many North Carolinians could be without power in extremely low temperatures” on Sunday. Mr. Cooper said several counties were opening warming shelters.

The storm system also spawned at least one tornado in southwestern Florida on Sunday morning, the Weather Service said. There were no reports of deaths, local officials said.

Three people were treated for minor injuries, and there was widespread damage, including to 108 mobile homes in three parks in the Iona McGregor area of Fort Myers, Fla., said Richard Rude, a meteorologist with the Weather Service in Tampa. About 200 people were displaced, local officials said.

Rodney Wynn, a meteorologist with the Weather Service in Tampa, Fla., said it is common for winter storm systems to cause “severe weather outbreaks” in the South.

As the storm moved toward the Northeast on Sunday afternoon, it was expected to remain inland, meaning cities closer to the coast, from Washington to New York City and Boston, will primarily receive heavy rain, Mr. Otto said.

Significant flooding was possible in parts of eastern Long Island and coastal New England on Sunday night and into Monday morning, he said.

By Sunday morning, more than 1,000 flights had been canceled in the affected states, according to FlightAware.com, which tracks delays and cancellations across the country.

Elsewhere in the South, northeastern Georgia and the Carolinas were expected to bear the brunt of freezing precipitation on Sunday, meteorologists said.

In Georgia, the Department of Public Safety reported several examples of drivers losing control on icy roadways, and officials said that road conditions would worsen through the day as strong wind gusts battered the state, hindering efforts to clear the highways.

Crews in South Carolina and Mississippi were also working on Sunday morning to clear highways. Videos shared by the states’ transportation departments showed highways that were covered by snow and almost entirely clear of vehicles.

On Friday, Gov. Ralph S. Northam of Virginia and Gov. Brian Kemp of Georgia joined Mr. Cooper by declaring states of emergency.

Virginia transportation officials were caught off guard this month when a storm stranded hundreds of drivers on Interstate 95 south of Washington.

Grace Ashford contributed reporting.