In my working life mud is a constant factor.
We dress for it. Wellies are excellent, muck boots are better. Gaiters can be a godsend, but are truly dire to get off if they're the buckle on kind. Don't wear expensive 'breathable' caghoules, they just clog up. Wear something you can sponge down at the end of the day and hang up to dry. Wax jackets are really good, they wipe down and dry off with paper towels. Sorted for the next day. Unless it's pouring too. Wax jackets aren't really designed to keep the rain out, not really. Too many are 'country fashion' style instead of the ultimate practicality style.
British army surplus kit works in the mud
Baby wipes are awfully usefuI even if I loathe the damned things, because they really aren't 'disposable' as claimed; they're plastic re-inforced.
One of those big cheap and cheerful car washing sponges (4 for a pound, pound land) is a brilliant mud cleaning off tool. That and any water you can get hold of. Rain, a field drain, a ditch, a burn, even a settled puddle, the sponge gets rid of the mud.