Never clean your bike by "blasting it with a hose." You stand a real good chance of contaminating parts such as the b.b your hubs etc. There are sveral companis that make long bristle brushes that will get alot of whatever off of your bike.
HTH,
May I reccomend that you not show fences "what's up." Some people run livestock on properties (like us) and fences is what keep them there. Anyway there are many tires that work well in mud. IRC Mythos work real well, Hutchison Mosquito Gold's work real well also. Theses two are from personal expwerience and the Hutchinson I ran through mud yesterday and they barely gummed up.