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.

The storm dumped as much as 6 to 7 inches in parts of central Oklahoma and northern Texas — canceling classes for more than 1 million students — before pushing into western Arkansas, according to the National Weather Service. Heavy snow fell in Little Rock, Arkansas, and further south and east into Louisiana, Mississippi and Alabama a wintry mix of sleet and freezing rain glazed roads and made travel treacherous.

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 3,800 delays and 1,800 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.