Like waresbear said, make sure the water is clear of suds.
Also, when you rinse off one side of a horse, make sure you go back and re-rinse the other side because the suds from the first side will spray over to the other side. I read in a book one time that when you firmly pet the coat, you should hear it squeak a little bit.
Just be warned, and you probably know this. Don't bathe your horse too often, even if you show a lot. It really dulls the coat. Usually if I have a show two weekends in a row, I only bathe once, and keep him covered with a fly sheet when he's in the pasture. Hosing him off with water won't dull his coat, but putting any soap in his coat will. Unless the horse is muddy or stained, don't wash him again if the shows are close. A quick hosing is usually enough.
Riders aren't 16 and pregnant. Riders are 16 and arthritic.