A whitener is NOT the same as a color enhancer shampoo (which usually contains some form of mild dye). It is merely a cleaning shampoo whose ingredients are hyper-focused on removing yellow and green staining and oxidation from white hairs.
So can it bleach your horse? No. There are no bleaching/dying ingredients in Vetrolin White 'N Brite. When in doubt, always look at the label. Unless it contains dyes, bleaches, or peroxides of some kind, it can NOT actually change the color of your horse. Most whitener shampoos (this one included) work of the premise that purple/blue scale cancels out green/yellow. This is how you get rid of manure stains on a white horse. Although the shampoo is a very dark purple or blue, it will not do anything to change the colors, even if you were bathing a black horse with it.