Be flexible. There are two main routes across Texas east to west. I-20 across north central TX merging with I-10 out toward El Paso. And I-10 across south Texas. I-20 would be the shorter route. We don't get a lot of ice/snow in this area. But it does happen. And it does sometimes happen in December. The good news is that the highways are rarely a problem longer than 2-3 days.
But even I-10 farther south can also get its share of ice/snow, especially out west of I-35. Once again rarely a problem more than 2-3 days.
But there have been many years when you could go across I-40 thru OKC and the TX panhandle in Dec and not see snow.
Just have to keep up with the weather forecast and be prepared for unplanned stop overs and/or route changes. You could start out on a shorter more northerly route and drop to the south as needed. There are lots of options at getting from one interstate down to the next one.