Equestrian helmets or plainly horse riding helmets are worn by horse riders to protect themselves from head injuries. In my personal opinion, it should be made compulsory by law just like helmets used in bikes.
In these Equestrian helmets, aerodynamics is not much of a factor. But safety and looks are more important factors. Outside the hard shell, there is normally a resin or plastic, sometimes covered with cloth to make it more attractive.
There are certification for helmets like ASTM/SEI (American Society for Testing and Materials / Safety Equipment Institute). Only the certified helmets which have undergone the necessary crash testing should be worn.