wait till the mud has dried and brush off, you can get rubber suede brushes, (or a dandy brush), then spray with a good silicone proofing spray, you can get that from outdoor shops.
I love my dublin boots. Very, very comfy. Not certain they are 100% waterproof but they are pretty good. I have sponged them off & then put on waterproofing leather conditioning stuff. you know the ones that you get from the people at big shows who offer to clean your boots for you!!