A helmet for beginners or a hat for more experienced riders are almost obligatory. In any case, highly advisable. And not for reasons you have probably thought of. Out of many falls off a horse at Geronimo, the helmet was useful maybe once. The real protection a helmet gives is from the branches under which we normally go. It's an irreplaceable tool for protection of your face and eyes from the branches during riding.
Riding helmet - yes or no and why?