I'm not good at interpreting dreams, but I also had a zombie dream a while ago, it definitely stuck in my memory, the way I was "killing" them was to use a sword. I was like the hero of the dream though. My therapist said it could mean that I am over coming fears and anxieties (in my real life I do not believe in zombies lol).

I also have tornado dreams once in a while, for me they are always in the distance. Like I see the tornado pop up, but they don't hurt me.

Dreams can be weird right?