What, to you, is bad weather?
The whole country is hot in summer, if that's bad.
From Florida to central Texas there is a hurricane risk for most of the year, but you avoid hurricanes by watching the forecasts, not going through at the same time.
Thunderstorm and tornado season across the south is October through April, these are shorter length events, but forecast only a day or two in advance. In Texas along the I-10 route, that season may be more like September-November and February-June, December and January the bad weather is ice storms.
I do my traveling at all times of the year, frequent trips to destinations from central Texas to central Florida, all through the southern states in between. The way I handle weather is to watch the 2-5 day forecasts, plan my moves for when the weather is clear, sit out the episodes that will make travel uncomfortable (ice, snow, major frontal systems producing severe storms, hurricanes). If I have my house with me, short waits are no real problem. Using motels, I tend to get grumpy about waiting an extra day.
Avoiding high temperatures, a lot harder to do, I don't really try. I am accustomed to living where daily highs will go into high 90s to low 100s for two to three months. That's body temperature, actually quite nice if not in the sun, and not exerting one's self.
Tom Test
Itasca Spirit 29B