Cleaning:
Yes, you should wash it off. The mud will hold moisture and cause corrosion. Mostly a problem with electrical connections, etc.
Pressure washer is the easiest way.
Prevention:
Don't off road it!!! There isn't any way of stopping the muck getting in there. You either have to grow up and stop jumping in puddles (if you're like me, you will never grow up!!!) or accept you will be cleaning it after each outing. :D