(CNN) — More than 1,000 Monday flights have been canceled in the United States as winter weather moves through the middle of the country.

Most of the cancellations so far are affecting Dallas Love Field and Dallas-Fort Worth International airports in Texas.

As of about 5:30 p.m. ET, just over 1,000 flights within, into or out of the US had been canceled Monday, according to flight tracking site FlightAware, with more than 4,100 delays.

About half of those cancellations are Southwest Airlines flights. The Dallas-based airline, which had an operations meltdown over the holidays, had canceled about 12% of its Monday schedule — about 480 flights, according to FlightAware.

Southwest Airlines did not immediately respond to a request for comment. As recently as Monday morning, CEO Bob Jordan was outlining fixes to prevent a repeat of the airline’s Christmas travel meltdown.

By contrast, fellow Texas-based carrier American Airlines canceled 6% of its Monday schedule. American had canceled about 200 US flights by 5:30 p.m. ET Monday.

Regional carrier SkyWest had canceled more than 140 flights.

Cancellations were already piling up for Tuesday flights, with about 800 canceled system wide by early Monday evening. Southwest and American had already canceled 8% to 10% of their Tuesday schedules.

In addition to widespread cancellations in Dallas on Monday and Tuesday, about 200 Monday flights were also canceled in and out of Denver International Airport in Colorado. For Tuesday, more than 100 flights in and out of Austin, Texas, had already been canceled by Monday evening.

There’s a winter storm warning in effect for a large portion of Texas, including the Dallas-Fort Worth area, until 6 a.m. Central Time on Wednesday.

Weather waivers for travelers

Southwest Airlines issued a winter weather waiver on Sunday and had extended waivers by midday Monday to a dozen airports in Texas, Oklahoma, Tennessee, Arkansas and Kentucky. The latest waivers apply to travel from January 30 to February 1.

American Airlines issued a waiver on Sunday for Dallas-Fort Worth International Airport (DFW) that applies to travel from January 29 to February 2.

Delta and United have also issued weather waivers. Their Monday operations were not significantly impacted by cancellations.

Dallas Love Field tweeted on Monday that its team “stands ready to treat and clear surfaces to allow for safe operations.” DFW was also preparing for bad weather.

Both airports urged travelers to check with their airlines for flight status before going to the airport.

Dangerous driving conditions

The weather will also make for treacherous road conditions. Up to a half an inch of ice or sleet is possible in parts of Texas, the National Weather Service warns. Ice accumulation is expected across at least 15 states, the National Weather Service’s Weather Prediction Center said.

“If you must travel, slow down and use extreme caution particularly when approaching bridges and overpasses,” the Texas warning says.

Motorists are advised to have a flashlight, food and water in their vehicles in case of an emergency. Here’s more on what to pack for winter driving.

Top image: Motorists in Dallas face wintry conditions. Credit: KTVT

More than 1,000 US flights canceled as winter weather snarls travel