I have lived in the southern end of tornado alley for all my 71 years. Last time our house was damaged by a tornado was in 1948. Can't remember the last time one hit any where in our town, but long, long time ago. Have actually seen only 3 in my lifetime.
Last year there were about
40,000 traffic deaths on our roadways. There were
17 tornado deaths. Be aware of approaching storm systems, but worry far more about traveling on the highways than about tornadoes. Tornadoes always make large headlines, but actually affect a very tiny fraction of land. Of course, that is of little consequence if you are on that particular fraction of land.
When you check into a park, ask about on site shelters available in the rare case of a tornado. If none available, know where the nearest most sturdy building is located, a concrete block restroom for example. If nothing at all available at the park, then know where you may safely go before a potentially violent storm arrives, such as a big box store. Have a good weather radio. Have a good weather app and radar on your phone. And keep up with weather forecast on TV. Be prepared but don't fret over it.
And by the way, Texas annually has the most tornadoes, more than twice any other state except Kansas. Of course, that relates to the state size.
Annual tornadoes per state