My Appendix QH was on stall rest for several weeks with a soft tissue injury. Once our vet cleared him for some light riding, I started him out at about 15 minutes of walk/trot. He was also able to go out in the paddock for a few hours by himself or with one quiet buddy.
My horse was in his late teens at the time, and he was as quiet as could be. No spook, no bolt, nothing. Dead quiet. We were trotting around the ring, and he noticed a patch of grass near the edge that was particularly enticing (the paddock is fairly grazed down, so it makes for a great transition lot when you're adjusting a horse to being on grass again). He reached down to grab it, and I pulled his head back up. He threw a tantrum and bucked me off.
I landed on my head and face, but luckily my helmet protected me. I walked away with sand in my jeans, and that's it. He's 22 now, and I STILL where a helmet every single time I ride him. You never know if they're going to spook, buck, trip or fall. Just because they're old and quiet doesn't mean you can't get hurt!