Bear, you and I seem to have a similar off roading history. I got my first off roader in 1972 and have been riding various dirt bikes ever since.
I'm not worried so much about having to clean out the mud, I have a Karcher pressure washer that's brilliant. However, if the oil cooler and radiator are clogged with thick gooey mud that dries in place and I have to then ride the bike to work until the next weekend before it actually gets a wash, then it could perhaps make the bike run hotter, which I believe it did for the last few days of commuting. The fan was on much more often and for longer than is usual, we had less traffic because of school holidays and it's coming into winter.
Mick
