Welcome to the worried mom's club. I have five kids and regardless of what sport or activity they are doing your going to worry, it comes with the parent title. Riding horses is a high risk activity for any one of any age, as parents we access the risk and then make sure our kids are as safe as they can be but accidents happen. Falling off is part of riding horses; helmets, broke horses and good instructors minimize the risk but you will never eliminate it, you have to accept it.
To curb my anxiety I have had to stop thinking about worse case scenarios, I just don't let them into my head any more. When I start feeling anxious I take a breath replace the thought with the exact opposite thought, it works for me. But you will never stop worrying about your child, it's what makes you a great mom.
Cheers to all the great moms who sit on the side of the arena and hold our breath watching our kids go over jumps, race around barrels, chase cows and when they fall off brush the dirt off dry the tears and watch them do it all over again.