Wow, I think I am one of the few with a naturally clean gray horse. Even when it's muddy outside, the most he'll have is a small-ish mud patch on one hip or his belly. In all the years I've known him, he's never been completely covered in mud (short of the one time I got him bogged completely down in a creek bottom while riding).
I wonder if it might be something about my dirt though. I turned him out the other day when he was still wet from a bath. He rolled on both sides and the next day, he looked as clean as he ever was.