Yes, white does exist in horses. It is called 'Dominate White' and is a genetic mutation of the Kit gene. It causes a white coat, pink skin, and brown eyes. There are also other forms of white caused by the Sabino and Splashed white genes (this can also cause blue eyes instead of brown) .
White is not to be confused with Grey where the horses coat turns white over a period of time. (They have grey skin under the hair.) Or Double Dilutes, such as cremello, perlino, and smoky cream. These horses have pink skin, blue eyes and an off-white or creamy colored coat.