Why aren't pure white horses rare?

White horses but can often be mislabeled, here is the run down.

Albino: This does not exist in equines, though some people will argue otherwise, albinism has never been documented in horses.

Grey: This is a color modifying gene that turns a horse 'white' with age, though this is not truly a white horse. A grey horses will have dark skin under it's coat.

Maximum white sabino: Technically yes this horse is white, usually has pink skin and might have blue eyes, but it's really a pinto with no visible color on it's coat.

White Spotting/ White Mutation/ 'Dominant white': Truly white horses caused by a genetic mutation, there are multiple forms of this mutation found in many breeds. Typically these horses have pink skin and brown eyes.

Double Dilution: This is caused by two copies the cream gene, it washes the coat color out to a very pale creamy white color and causes blue eyes. However the horses is not white.