Amarach Acres, after reading your posts, I wondered if we had the same child. Except mine is now 21. I will share what we learned over the years in hopes to reassure you that it does diminish somewhat as they mature. There are a lot of medical studies and peer reviewed articles addressing pediatric pain responses. It is actually very complex as there are physical pain factors along with psycho-social behavioral responses.
Generally speaking, children learn early on which of their responses gets them the most attention. This starts in early childhood and the best example I can think of is the parental response to when infant/young children get their immunizations. A first child is going to get a lot of attention when they cry after their shot as it is also a first time experience for the parent. Let’s say, By the third child, the parent knows the drill and parental response is different and more than likely not as intensely over protective. So birth order plays a part, parental response plays a part and the payoff for the child plays a part. Basically, the more dramatic the pain response, the more attention the child receives, especially when they learn it in their non verbal years. Which can’t be helped! Personality plays a part too. There is a payoff for each child in the parental reaction to their pain. Also, fear of pain plays a part too. When a child sees the syringe and needle come out, they anticipate and associate it with pain.
Using your example of a fall off the horse and the subsequent reaction of your daughter (which mine has also done), her age, personality, gender, birth order, fear and the parent who witnessed the fall and their reaction all came into play. I learned to let the trainer deal with my daughter and not react or come rushing into the ring. If I was needed, the trainer motioned to me. Over time, her dramatic pain responses diminished as there was praise from the trainer for getting back on and I didn’t feed into it. I also learned that when she was quiet, I knew she was hurt.
Each child is different. When my daughter was little, she would see a speck of blood and come crying to me that she was bleeding. I had to take out a magnifying glass to find it. The payoff: my attention and a bandaid. Eventually, as she got older, I would tell her “all bleeding eventually stops”. Her pain response is much different when her friends are around versus me. She brushes it off amongst peers and looks “tough”. I just look at her and say “Seriously?”.
It will get better as she learns that her parents don’t feed into it, positively or negatively. Peer pressure will help. You will be able to ascertain when it is serious and need to act or get medical intervention. A quick observation, by you or the trainer, of her moving all limbs, no deformity and weight bearing is a good indication that she is probably ok. I simply would tell my daughter, “I’ll meet you at the car when you are ready”. 
