Many other birds stay right around here in north Texas, including Cardinals, Mockingbirds, Chickadees, Robins and most woodpeckers.
Sadly, wild birds have a high mortality in cool weather. This is mainly from exposure to weather, coupled with a lack of fresh, energy-producing foods. To combat this, they seek out "roosts" for the night - places to get out of the wind and weather. This can be almost anything; an evergreen tree or even an unused birdhouse. Provide plenty of good food too. And leave your birdbath out so the birds can get clean (helps them stay warm).
North Texans have been doing a good job of providing these basics, so we continue to have more birds here in cool weather, than in spring and summer.
(Incidentally, other birds that usually come here for the cool weather include Cedar Waxwings, Pine Siskins, Nuthatches, Yellow-rumped Warblers, Orange-crowned Warblers and Northern Flickers.)