DALLAS — Snow and icy conditions threatened to paralyze parts of the South from Texas to Alabama on Thursday, as officials closed schools, canceled or delayed flights, and warned residents in some of the worst-hit areas to stay off roads as a winter storm moves east.

Paul Kirkwood, a National Weather Service meteorologist, said the storm sweeping through the Dallas area will create a “swath of snow” as it moves through parts of Arkansas, Louisiana, Alabama, Mississippi, Georgia, Tennessee, Kentucky, North Carolina and South Carolina.

Charles Daniel, a truck driver hauling a 48-foot trailer in south-central Oklahoma on Thursday, said the roads were slushy and slick.

“I have not seen any accidents, but I have seen a couple of people get stuck out on the road and sliding around,” he said. “People do not need to be driving.”

The storm started dumping a mix of sleet and heavy snow Thursday morning in north Texas and Oklahoma, where schools canceled classes for more than 1 million students. Closures also kept students home in Kansas City and Arkansas, while in Virginia, frustrations mounted in the state capital over a boil-water advisory caused by an earlier round of winter storms.

Hundreds of flights were canceled by Thursday morning in Dallas, according to tracking platform FlightAware, with more than 3,100 delays and 2,100 cancellations reported nationally.

Road crews began treating roads in Arkansas, Oklahoma and Texas ahead of the expected arrival of as much as 7 inches of snow in some parts of those states.

The system was expected to push northeastward by Friday with heavy snow and freezing rain all the way to the North Carolina coast.