It it very unlikely to be killed on the ground, especially if you stick to well trained, calm horses. However, you have to keep your wits around large animals all the time as accidents can happen even with calmest of them. There was an accident last year in which a women was killed by a cow kick. Mind you, those are really, really rare. More often there are broken toes and similar injuries, but even those are quite rare. I've often seen people with broken limbs from falling off, but only one instance where a person broke something when handling a horse.
I just remembered that there are computerized mechanical horses, if you wish to start off on a very, very safe note.
All of this.
If you haven't already realized it OP, horses require your full attention 100% of the time. You cannot ever forget of the damage they can do. This doesn't mean you have to be tense, or stressed around them 100% of the time. Quite the opposite (they feed off your anxiety so that would just make it worse). But it does mean that you have to be PRESENT at all times. This is actually what I, and a lot of people, like about being with horses and riding them. You have to be in the moment, fully tuned in to what they are feeling, thinking, and you have to respect it. If you want to be safe and if you want your horse's full cooperation, you have to be totally focused on them. It's a type of energy you give off and receive from them, and when the connection is there, it is truly magical.
Whether I'm in the barn doing chores, grooming my horses, riding on a trail or focusing hard on more complicated maneuvers, I have to be tuned into my horse to have an idea (an inkling really, because it can all change in an instant) of what they will do next. That, to me, is the most gratifying feeling in the world and the best kind of therapy. I can't think about work, my kids, or anything other than my horse. That is a great gift in my view.