There's an old saying..
"If you don't like the weather in Texas, wait 20 minutes and it will change."
Our winter ice storms do take longer than 20 minutes to go away, and there's no way to predict when one is going to happen more than a day or so ahead of the event. We didn't have any of them last year, and some years we have four or five here in North Texas. A route farther south, like I-10 would help.
My advice would be to plan your trip with a few days extra in the schedule, so you could hole up in an RV park and wait out a few days of icy roads. Road conditions are by far the worst hazard. We don't get snow on the roads, it goes straight to black ice. Combine that with drivers inexperienced with severe winter conditions, and it becomes quite a show. Stay put and watch it on TV when that happens.