Here is my opinion on the matter. I think more, less severe injuries occur when riding in the ring (doing jumping or anything else). I think the most severe injuries occur on trail but they happen less often. Take your pick with the risk! In the arena you are jumping over obstacles, making tight turns, learning new things and could fall off. BUT the horse cannot get far in the arena. The footing is soft so it hurts far less when you fall in an arena, and there are typically many people around the help you if something happens. Also, you are probably not far off the beaten path if you are in a ring so if an ambulance is needed it can get to you. If you are out on trail, your horse can take off at any second extremely fast. Falling on the trail hurts much more than in the arena especially if you fall on some rocks. You may not have cell service and an ambulance may be unable to get to you.
Like many other people have said, just being around horses is dangerous for the reasons they said. In my opinion, you just have to love horses enough to take the risk. I just found out that I might have to have surgery in the near future and the very first thing that came to mind when I heard that was, "How soon will I be able to get back to riding?" It's my life. I'm not complete without it. Any and all risks are 1,000% worth it to me. You have to decide if it's worth it to you.
You can never fully avoid danger, but you can definitely try to prevent it. Make sure you have your phone securely on you and not your horse when you go out. Make sure you go with someone or tell someone where you are going. Use common sense when riding. If you think something might be dangerous, don't do it. Always wear a helmet that fits you well and is not old and make sure you ride a horse that is not generally spooky or hyper.