Yep, I leave everything on. simple green makes the engine look like brand new. I just put a rubber cap on the exhaust and zip tie a plastic bad over the air filter (I use motor saver air filters)

A hair dryer will dry it up real fast and keep stuff from rusting.
Also be sure and wd-40 pretty much all the bearings, even the clutch bell can take a little squirt from the outside. They need this even if you don't get them wet just because of the moisture from the mud.

Later
Randy