Just wanted to wish you well, and offer that therapeutic riding centers are wonderful places, as either a participating client or volunteer. I have been involved as a volunteer with two top notch places over the years.
I would recommend that when you go to the barn, ask to meet an experienced volunteer to "shadow" him/her for a couple of days. You want the person who knows the horses' personalities and can tell you, "oh, Tinkerbelle will try to get away with pulling her foot away when you clean it," or, "Secret is perfectly happy being groomed and led around on the leadline when you need to calm yourself down." A fellow volunteer who's been there awhile can talk to you about the routines of the barn and help alleviate some of that newcomer anxiety in a way that maybe the program director or barn manager can't. Ask lots of questions. See if one of the experienced volunteers will give you an email/phone number in case you have follow-up questions after you've gone to the barn a couple of times. I suggest all these things because this is what I offer to new volunteers when I join the volunteer trainings, and I'm always thrilled when someone is interested enough to take me up on it!
Also, know that volunteering in a lesson doesn't require you to lead/handle the horse if you don't want to. Depending on the individual rider's needs, therapeutic lessons often require one leader/horse handler, and 1-2 "sidewalkers" who hover alongside the horse near the rider's legs to provide additional stability/support if needed. So, you could be near the horse without being in control, and because your focus and attention belongs on the rider, it may take your mind off any nerves you have about being so close to the horse. Obviously you don't have to do that until you're ready, but I thought I would mention the different ways to participate in the lesson.