Horse Racing and Zebras

Question
Hello, Hope you can help me.   Just wondering if it is legal for Zebra's and their hybrids (even with a horse hybrid) is allowed to run in a horse race.   I did some checking and found out that Zebra's (and assuming hybrids) are faster then horses (if my info was correct).  This leads to a more general question if their is another equine (non-horse) breed which is faster would that breed be allowed?

Answer
A "horse race" could involve any race between equines.
The Thoroughbreds must be thoroughbreds registered with the Jockey club.
The harness horses must be standardsbreds and registered with their association.
The same is true with quarter horse races.
They also have arabian races for Arabian horses and mule races for mules.
If they had enough zebras that people wanted to compete, someplace would have races for them, but they do not mix the breeds in the same race.
I hope that explains it for you