If I were in this situation, this is what I'd do. I would cancel the show in its enitirey. I wouldn't risk my professional reputation, no matter how sensible the decision is (preventing a spread of disease), there is always going to be rumors flying about the "real" reason you asked this person not to attend. People are fickle, and I have found that my friends who I thought were my close confidants, turned out to be my biggest enemies!! Even though there are real health issues to look at, conjured up gossip may consist of "you feel threatened by her" "you are eliminating your competition" etc, etc, etc! It's like poking a stick in a hornet's nest to me. It's your show and your decision, but through my experience, cancelling would be the easiest, most diplomatic solution. She may end up with hurt feelings over it.
Plus, not having her there is no garuntee the horses will be safe. Anyway, Good luck!
