Ride with a helmet, ride without one, your choice. I choose to ride with one because I feel safer that way. Yeah, I could still get hurt, but I could get hurt worse without one. It's not a "false sense of security" for me, because I know that if something happens, my helmet might not really help. My mom prefers to ride without a helmet. My BO is probably 5ft, if even, and her horse is 16.2 and she NEVER rides him with a helmet. She's had a horse flip over onto her, and still, no helmet. It's a personal choice and although we wish that we can make others do what we believe, they won't because they make their own decisions.
As far as horses being dangerous to ride... they are extremely dangerous! Yet again, everything we do is dangerous, from walking across the street to getting in the car to go to the grocery store that is 2 miles away. We choose to get on a 1200lb animal and make it do what we want, not what the animal wants. So, yeah, that tends to lead to some issues. For me, however, I love it so the chance injury is worth the risk.