Do horses get STDs?

Yes - there are a few things that can be sexually transmitted in horses, including sometimes via AI (AI can both reduce the risk and increase it).

The most common is Contagious Equine Metritis - inflammation of the uterine lining that can cause miscarriage and lower fertility. Other bacteria can cause inflammation of the uterus or the placenta. Stallions carry the disease but show no symptoms.

Other STDS include EVA (which still gives me personal nightmares), dourine (which thankfully is rare) and, yes, herpes.

Horses do not, however, get anything like AIDS.