What do we do? Stop riding, and spoil dreams? Keep riding, and risk wheelchair/death? If something happened, I could not live with myself.
As a parent I totally understand your fear and concerns. I had my kids involved in everything from horseback riding, snow skiing, water skiing, rock climbing, surfing, scuba diving, hiking, BMX racing and motorcycles of all kinds, oh and skateboards those little things are really dangerous!
All I can say that I learned as a parent is yes they will get injured and maybe not participating in said sport but just walking across the street! You really never know and you can't keep them in a bubble, darn!
The best thing is to make sure they are fully aware of the how's and whys of every sport. That they wear all the protective gear available and have first rate instructors!
Then the hard part as a parent is to not let them know you are fearful, they will have their own fears to contend with and if they even sense you are fearful they will be concentrating on YOU and not on the task at hand. One of my kids coaches told me this and to always send them off to have fun! Do not show your concerns or even voice them except to maybe tighten up the helmet a bit and give 'em a pat on the rump or if no one is looking a hug.
Out of 5 kids one broke both arms skateboarding and one leg too and not at the same time. He also broke his wrist falling off a wall. He also knocked out his front teeth playing tether-ball. Oh vay! Let see a couple of sprained ankles with two of the kids, they are as bad if not worse than a break imho. Some minor stitches from goofing off, can't remember how that was done but nothing to worry about.
Seems to me if you get them up and raised out the door on their own the worry doesn't stop there and then they go and add to it with their own kids (grand kids) who are off and running as well.......sigh it never stops and life is messy, you just hope for the best and if you're lucky (yes I said lucky) all turns out well and no one is worse for the wear, maybe a few shattered nerves but that's doable.
Hope your kiddo has lots of fun on the horse. I used to love riding horses myself and got thrown a couple of times barely missing a bolder with my noggin once, *ouch*! But it didn't stop me from riding I just held on tighter! LOL