It's normally a smaller ugly wheel, but I did buy a stander lancer evolution from the UCD that keeps the same wheels it came with when you switch to dirt or snow, but I think they are still smaller diameter.
The reason behind this is that dirt and snow tires larger aspect ratio, meaning taller sidewall compared to width. That would force you to have a smaller wheel to keep the same outside diameter of the tire.
Nope, even having custom wheels can't take away this. I once had an R34 with JS+M's and then when I went to my custom snow track, it was the usual rally rims instead of the Enkei ones.