The basic part should be to use a moving/animated texture on a polygon grid wich you deform so that it fits the corners, that is nearly equivalent to what you do when moving textures for a river - the uv-map looks like a undeformed version of the model.
Then you can add more small streched sprites to get some volume into the effect.
Using a soft particle shader to prevent a sharp intersection between fog and geometrie would also be a good idea