Orvus paste shampoo was key for my mostly white Paints! Followed by Quicsilver whitening shampoo only on stubborn stains or yellowed tails. You can use Quicsilver everywhere, but it dries out the hair which leaves it dull.
Clipping the legs helps keep them cleaner during the spring/summer - shorter hair means less hair to get/show stains. But that does remove some natural protection, so while it's common practice with show horses, it's probably not a good idea for trail horses who ride through heavy brush nor in the winter where hair is needed for warmth.