We have done this method alot this time of year when the mud is unbelievable and mudballs are just what happens to cattle with hair:
Use buckets of really warm water with Dawn dish soap to soften them up. Then we get 2 people to sit on buckets on either side, with sharp pocket knifes. Split each mudball in half, then soak some more. If they are really bad, squirt a little dish soap on each and every hairball. Sounds insane, but with about an hours work, 2 people can open and soak off the mud and save the hair with a little elbow grease. I know this sounds crazy, but we have had to do this before. Hope you can find a warm shed to do this in!