Ditto. Anything waterbased & also recommended for children's face painting (NOT the greasy clown-makeup kind of stuff). I would also make sure that the horse is clean but not freshly bathed. He'll need to retain some natural oils on his skin to make the removal easier. Hope he doesn't wind up having allergies! I would explain to her the potential pitfalls of painting her pony & make sure she understands that you cannot be held liable.
If you do this, ya gotta take pics!

Would love to see a painted pony! (Poor thing.)