I just did this for a costume class with my mini! (Except I turned my entire horse pink and she was a My Little Pony instead.) I went to the local hair salon and bought some TEMPORARY hair coloring spray. It was the stuff for halloween and parties. I made sure to spot test a small area under her neck to check for a reaction. There wasn't any, and it washed out very easily with water afterwards.
People also have used kid finger paints, which would be another option. My sister did that to one of our grey Quarter Horses for her college art class. The finger paints actually curried out really nicely.
The only thing I strongly recommend to NOT use (besides permanent paints or paints that specifically say to not put on skin) is the paint made specifically just for horses. I don't remember what it is called, and I don't think I am allowed to say it's name on here anyways. My neighbors used the horse paint on their mini for a costume class and it did not come off for over a month. Same thing happened to my friend, and she couldn't get it off no matter how often she washed her horse.