Been my experince that anything that moves and is packed with mud will soon fail. Most mud is mixed with sand. Pressure wash everything, check for mud traps, those places it gets into and doesn't want to wash out of, like the bottom of the rear quarter panels, inside the door bottoms etc.
Wash out the alternator, the starter and the radiator etc. even around the brake calipers.
If you don't get the mud out before it dries, it sure doesn't get any easier to clean later on.
If you leave the mud anyplace until winter, salt can get mixed in and stuff will start to rot really quickly.
If you clean it out before it has time to cause any serious damage you are going to save yourself many headaches, time troubleshooting and a bunch of cash later on.
Mud is fun, cleanup is a pain, but if you do it often enough it gets easier with a plan and practice.
I'm persona non grata at most of the local quarter washes.
