They also said that several trees had broken down and two houses had been damaged due to falling trees.
The National Weather Service in Dallas confirmed a tornado in Corsicana, probably of EF0 intensity on the Enhanced Fujita scale, with winds of 65 to 85 mph.
Corsicana is about 50 miles southeast of Dallas.
Snow, ice and torrential rain are also expected in Texas and Oklahoma
In addition to the heavy storm, snow, ice and rain are expected in the region in the coming days.
Nearly 8 million are at risk of snow and ice from western Texas to western Oklahoma during Thursday night. The accumulations can be more than 30 centimeters in western Texas and at least 15 centimeters in western Oklahoma and Kansas.
Up to a quarter of an inch of ice and possibly more is possible for parts of northern Texas, central Oklahoma, eastern Kansas and northern Missouri.
On the hot side of the storm, heavy rain is expected in Arkansas, Texas and Louisiana by Friday, with about 7 to 15 centimeters of rain.
There is growing concern about the possibility of damaging tornadoes and winds starting on Thursday afternoon and lasting until after midnight with the dawn of the new year. Almost 18 million are at risk of bad weather.