That's what I mow the most with my brush hog!
10" of annual precipitation is a wet year for us. Most who live East of I-35 and West of the Sierra Nevadas wouldn't understand.
I cleaned most of it with a 1 gallon weed sprayer, 25% mix of Purple Power, plastic putty knife, and a nylon brush as I don't own 600 ft of garden hose to get water to it. After 1.5 hours and about 10 gallons of water through the weed sprayer it was clean enough I wasn't afraid to tear it apart. I then sealed the differential underneath with RVT and lightly bolting down a corrugated plastic campaign sign that I collect after every election cycle. They are great for things like this, and to use as target backers at the range.
Fall is the worst time for mowing. Once everything dies and drys up, the radiator plugs quickly with dust and dried plant pieces. Once it starts to get up there in temperature and I stop to clean the radiator I'm done for the day. Until it dries out completely all the moisture from washing out the radiator does is cause it to plug up faster.