Yes, a white horse has won the Kentucky Derby if you interpret white as 'roan' or 'gray'. According to those criteria, there have been eight [8] such winners:
1. Determine [1951 - 1972], gray stallion winner in 1954;
2. Decidedly [1962 - ?], gray stallion, in 1959;
3. Spectacular Bid [February 17, 1976 - June 9, 2003], gray stallion in 1978;
4. Gato Del Sol [February 23, 1979 - August 7, 2007], gray stallion, in 1982;
5. Winning Colors [February 14, 1985 - February 17, 2008], a filly that officially was described as a 'roan' but actually was soft gray with a white face, in 1988;
6. Silver Charm [foaled February 22, 1994], gray stallion, in 1997;
7. Monarchos [foaled 1998], gray stallion, in 2001; and
8. Giacomo [foaled February 16, 2002], gray stallion
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7 Greys have won the derby:
Determine (1954)
Decidedly (1962)
Dancer's Image (1968)
Spectacular Bid (1979)
Gato del Sol (1982)
Winning Colors (1988)
Silver Charm (1997)
It's a bit of a trick question, all horses in the Derby are 3 yrs of age and no more, no less. Female horeses aren't called mares until they reach age 5. So the short answer to the question is, "None."
There have been 3 female horses win the Derby however--referred to as a "filly"before age 5. They were: Winning Colors, Genuine Risk and Regret.
No, the only horses that can run in the Kentucky Derby, or any thoroughbred race, must be full blooded thoroughbred with proper documentation of the horses registry.