Mia wasn't a race horse, but she was and is a pretty intense Arabian mare. Since she didn't know to pick her feet up over small rocks, I assume she had no trail experience. I rode her bitless for a few years, with her nerves getting worse and worse, until I finally gave her a break for 8 months. Then I hired a trainer, who concluded she had never been broken to ride at all (and she was sold as 'perfect for a beginner'). Maybe the fact that they wouldn't let me lead her, and only allowed me to ride her in a tiny 30' round pen should have been a hint...
Anyways, she is getting better. I find that about 50% of what she can give me when I lead her is what she gives me when I'm on her back. But it sure as heck helps to have that 50% down pat BEFORE I get on her back!
Riding - she prances a lot. When she gets nervous, she wants to go. There is a balance there I sometimes miss. Restrain her too much, and she gets nervous. Don't restrain her at all, and she may wind up to a bolt. Some restraint is right, but how much? As a general rule, what does NOT work is trying to constantly hold her in. But after almost 5 years, it is still a challenge.
However, she is the horse that got me interested in riding. She is so strong willed, and so willing and eager to please when not nervous, interested in everything...she is too much horse for me, but no one else wants her and I genuinely like being around her. The trainer I hired said Mia was lucky, because she had a lot of clients who would have dumped her at an auction by now.
Relaxing in the saddle - always tough. I'm not sure I will EVER really relax on Mia. She hasn't done a true bolt in over a year, but the "OMG Crouch" comes very regularly. I wish there were cattle for her to work. I think riding down the trail gives her too much time to imagine things.
I use an Australian style saddle with her. IMHO, they are the easiest saddle to stay in when the horse hits the fan. Like one ad I saw said, "The only thing that can force you out of this saddle is starvation!" Well, maybe they aren't THAT good, but I like them.
This is a good video on a 'Pulley Stop'. I almost never resort to this, but it once kept Mia & I from hitting a sharp turn covered with rocks at a full gallop:
Emergency Stop on a Horse - Pulley Rein - YouTube
Good luck to you! Keep us informed.
Oh...and singing. Something the trainer told me, probably because she got tired of hearing me sing, was to try breathing in audibly, hold for 2 seconds, then audibly exhale. It really does seem to help Mia calm down.