There is no law requiring the use of helmets when riding horses, only a requirement if participating in USEF sanctioned hunter jumper competitions and now USDF sanctioned competitions. If equestrians opt not to wear a helmet everytime they ride, they do so at their own risk.
I believe there is a law in New York State that requires a helmet for all riders under a certain age. 14? 16? Something like that.
I have no idea how much it is enforced, especially on private property.