Is it the whole snout area? Any bumps, raw spots? Hard to say what it might be or whether it is even from the mud. May be an allergic reaction to something. Was this in a yard or area that was possibly treated with chemicals? I would maybe try to wash it with warm water or maybe a mild soap and keep it dry. I would not try anything topical on it that just might make it worse. If it does not improve or looks worse, you should probably have your Vet check it.