I don't. They get wet and nasty looking and they get dry again too. I've read on BYC of folks having a problem with their feather footed birds getting mud balls on their feet, but I haven't had that problem.
My birds are mainly on pasture, but they do like to play in the mud and dirt.
It's 58 degrees right now and there's a steady rain. My birds are out playing and foraging in it. Their feet will look awful later, but it doesn't seem to bother them and they will dry when they go to roost tonight.