Shire horse people in this country use Persil washing powder for the feathers. They go manky yellow because of the clay in the soil. You need to do a spot test first tho', to see she isn't allergic. Listerine mouthwash is brilliant for stable stains (most of mine are grey) but I have never washed a whole horse with it. When removing stains, use one with the water and listerine/shampoo/soap to rub the stain, and use another directly underneath the area, with your other hand, to stop the drips causing yellow rivulets.
I know friends who swear by Cowboy Magic, but I use a cheaper "blue" shampoo alternative. One thing that helps quite a lot is to use one of those netting bath scrubs that you use with shower gel. That way you can get up a lot of lather and rubbing action, but without actually using a lot the shampoo or soap on the horse.
Greys are a lot of work to keep clean. I keep my stallion rugged all winter but just let him go au naturelle in summer when he is running with the mares, IOW, filthy.