My horse only has small facial markings, but I just use baby shampoo. This way if it gets in her eyes it won't sting. Then I turn the water on really low and she knows to drop her head so the water runs down her face and doesn't risk getting in her ears.
I just fill a sponge with warm water and maybe a teensy bit of soap and scrub my girls' blaze and nose. It works great. She's pretty sure she's going to drop dead, but she'll get over it eventually. =]
Self Rinse Plus. It is a self rinsing shampoo with a whiting agent. Spray some onto a cloth and rub the white spot in small circles. It will get very foamy. Then take a shammy and dry the face. Then redo it until it looks clean. Self rinse plus can be used everywhere. I use it on my chestnuts tail in the winter when I can't wash it. It is also great for touching up spots at shows!