As said above, just make sure that there's no clumps of mud and hair under the tack, then you're fine. Having some dust isn't going to kill him, and a bit of mud over his backside/neck isn't going to make him sore ;) Some people just feel the need to have a perfectly clean horse.... I must admit I am one of them, but rugging keeps him clean enough so I only give hi a quick once over with a brush before I hope on.
As for hooves, well I like to do them twice a day, but my paddock has a lot of clay in it and a lot of small stones so I like to have a look and make sure there's no rocks wedged under his shoe or next to the frog. Even if the bulk of the mud falls out on the road, if there is a stone wedged in there it's not going to fall out with the rest of the mud, so I'd definitely give them a quick once over before you ride.