You should do fine. Those kinds of things are scary at first, but if you take it in stride you will not only do great but have tons of fun the whole time!? The first barrel race that I ran, I was so so SO nervous but I just did it and let the horse make me feel better which seemed to make her feel better too. Don't stress to much or get too excited because the horse will react in the same fashion. Good luck and I hope that you have a great time.
"Do not -follow- where the path may lead. Go instead, where there is no path, and leave a trail." ~Ralph Waldo Emerson