The reason whitening shampoos are purple, is because on the color wheel, purple is the opposite of yellow, thus neutralizing the color. This is why when people (such as myself) use a toner (that is purple!) to get icky yellow out of their bleached hair, and to give it a platinum look. And actually, if the horse gets almost the lightest tint of purple, he'll dry OMGZ!White - I would know, 'cause I accidentally did it one time with Farnam's white n bright. Nothing else has 'toned' him like good old white n bright!
Got a gray/blue roam and want him silver/blue? Use a blue shampoo. It will work with the natural color of the hair to make him even more blue/silver looking.
I've got a lovely bunch of Neuticals,
There they are all standing in a row
Big ones, small ones, some as big as your head