You seriously need to have a sit down meeting with as many members as possible...as soon as possible. Let them know that the meeting is specifically intended to define your club rules, requirements and codes of conduct. ALL horseback riding should be curtailed during this meeting - the kids need to pay attention, too!
If your control doesn't establish some sort of control PDQ, someone is going to get hurt. I don't think the county will take anything but a dim view of things if such reckless behavior continues.
And, just to mention - it apparently does no good to yell at those kids. It's their parents you need to yell at. When my family were members of our local roundup club, members could be banned from riding at events for breaking the rules. Families could be banned from the club if their behavior, or their kids' behaviour, was a problem.