I have had tornado dreams most of my life. For me, as a kid ,tornadoes were a real threat and the only thing the adults in my life ever showed any fear about. Which made me more terrified of them. I believe, for me the dreams were about fear. If I were going through a lot of anxiety I dreamed about tornadoes or someone chasing me.
The most interesting thing is that when I actually witnessed a small tornado form in Florida, the terror of them disappeared. The tornado wasn't everywhere and after me, it was a force of nature that I had no control over. Once I accepted that fact I have hardly ever dreamed of them again.