I didn't read all the posts, so forgive me if I'm repeating someone.
I teach beginners, and one of my kiddos is 8. She is a GREAT rider. Has a very solid seat, does what I ask of her, and remembers it. She has her own horse who is not a dead broke babysitter like a lot of horses that kids learn on. Her horse gives her trouble sometimes, tossing her head, refusing to move, etc. She handles it like a pro, and gets her horse paying attention again.
However, if you put that kid on another horse - she cries. She gets scared. Doesn't want to ride. Doesn't want to do anything. It's bizarre.
Her parents have even called me asking why their kid is still scared of horses when they are paying me for lessons - and I don't have an answer for them. In our lessons, she's great, knows her stuff, and rides awesome. At home, she gets scared when her horse does something unexpected.
I haven't been able to get to the bottom of it. I think a lot of it is having a relationship with one particular horse, and the security of having an instructor present.
10 is very young still. I didn't feel comfortable around every horse until I was in my teens, and I've been riding since I was 5.
Some people need more time to be comfortable around all or most horses. Some little kids aren't scared of anything. Others need to be guided a little more closely through "scary" situations.
If she loves riding, there's no reason to let a little fear get in her way. Let her work through them on her own time.
Best of luck!