I always come in early to the warm up befor everyone else and just walk and walk and walk.Also then he doesn't get as tense and stiffen up.I also always lunge before and after all my classes. My horses have never pulled up lame or stiff. When I warm up I always do a loose rein (no matter what). This way my horse can stretch( witch for some reason he does fantastically with no force), feel as if he knows what to do and he can almost do it for himself, and just letting him see everything and take a deep breathe.
You can get a sounless fly veil witch blocks the sound and even on quit horse, it's useful.Also I just went to my first show with the my new 5 year old thoroughbred and he could not stand still, he was just so excited. I always( with every horse) take everything slow. When I unload from the trailer I immediately get him standing to make sure he is listening to me and won't just storm off.
I've been trying essential oils and all natural remedies because they aren't anything changing hormones it's more just helping improve certain things. Wild orange essential oil from dottera is good for reducing depression and anxiety which can help the horse stay calm and collected instead of being anxious giving them a reason to be spooky.
Try going to the show place a day before the show if they will allow it, some places do and other don't. The day before let your horse settle in for acouple hours and then after that ride the horse in the arena, or walk them around the new area. This will help them get a sense of where they are and realize it is ok.
And then the day of the show you can try earplugs, lunge them alittle, walk them around a bit if possible.