I know this isn't what you want to hear but:
1. Brush them until you feel like you need rotator cup surgery.
2. Then take the vacuum to them until you need a second job to pay the electric.
3. Brush again with whatever energy you have left, then spritz them with ShoSheen or whatever its replacement is in today's world.
4. If you have white legs and/or white on the face, use dry corn starch on any stains. It does a great job of removing stains on white or light colored horses.
I'm not kidding. That's what I did six hours before the Christmas Parade the year my horse found the deepest mud hole on the farm to roll in, then come sauntering up to the barn; proud as all get-out of how well he wallpapered himself in this Tennessee clay/mud
I spent four hours on him and that was his first introduction to a vacuum -- the Kirby from the house. I was so mad at him, I didn't care if the Kirby sucked him inside out. He knew I was mad and never flicked an ear when I connected a live vacuum to him