There is dog shampoo that you rub on then wipe off with a rag this works better than green out and miracle groom. Also for a brighter white you can use grooming chalk, baby powder or corn starch. Hope this helps.
I used a soft curry and what ever shampoo im using. If your worried about soap in the eyes... you can put some baby oil in their eyes. It will make a film that wont hurt the horse, but wont let shampoo sting the eye.