Nobody wants to fall. But anyone who rides horses very much will fall from time to time. Head injuries are the most common reason for horse-related hospital admissions and deaths. It's cool to wear a riding helmet because riding helmets work. A bicycle helmet will not adequately protect your head in a fall from a horse.
People fall off bikes and horses at different angles and in different directions.
A lot of scientific research has gone into producing helmets specifically designed to protect human heads in equestrian accidents. It's cool to wear a riding helmet because you may help save a friend's life. The people they ride with wear helmets, so they do, too. It's cool to wear a riding helmet because the life you save may be your own. Your life is precious.