A quick way to do realtime animated mist & fog is to use UV distortion and a scrolling "clouds" texture. Pretty effective if you tweak it. If you advance to about 0:16 in the video, you can see the maps that go into it.
https://www.youtube.com/watch?v=H2vLwOAu0UI&t=16s
There's a bit more about it on the first page of my sketchbook.