I have a gray horse, though he's mostly just white now, who's actually naturally a very clean horse. Occasionally, he'll end up with a green spot on his belly or hip from where he layed down on a poop pile, but that's relatively rare. The only time he ends up with the full-body mud mask is when there simply isn't a dry place to roll.
IMHO, unless you need
him to be sparkly clean for some reason (show, rodeo, parade, etc), then I just let them be a bit dirty. Sure, I curry off the excess dirt, but I don't worry much about stains.
As for the pink skin thing, he appears to have the typical Appy mottled skin on his face/muzzle. It probably wouldn't hurt to keep a fly mask with a nose cover or sunscreen on him in the summer, but you likely won't have the same sunburn issues as someone with a truly pink skinned horse.