The answer is: Yes.
Fortunately, there's now a vaccine for horses - the shot is generally given annually.
Also fortunately, most horses with rabies do not become as aggressive as, say, dogs that get the disease. Rabies takes two forms - "furious" and "dumb" - and only the furious form results in the extreme aggression. Horses are more likely to get the dumb form (but they certainly can get the furious form, which can result in extreme behavior changes).
The first symptom of rabies in horses is often colic and depression.