Two of my horses have lots of white, and one has none. I hardly ever give them a bath, and they usually keep clean unless they go in the pasture that is really swampy. I would not wash a horse's coat that often, as it removes the natural oils as the others said.
If anything I would brush the horse every day or so if there are bigger pieces of dirt it would be better for them. Sure, they might still be stained but it isn't good for them to get a bath very often. I have an Appy and a Paint, so there is alot of white. If you don't like riding a dirty horse, well, then don't ride horses. It is just natural for them to want to have the oils in their coat, and it isn't as nice for horses as it is for people to feel "clean". Some horses are peculiar and stay clean always, others just can't stand it. I am constantly brushing my horses. They love it, and it helps keep them somewhat clean.