Fear is a common emotion felt for first time riders, as well as seasoned riders. The most common fears are of falling off the horse, being hurt by the horse, or hurting the horse themselves.
Recently I had a young student ask me "how can I keep riding if I can't get over my fear?" She was afraid of letting go of the saddle at the trot, in order to slow her horse down with the reins. I asked her what she was afraid of happening, and she said "falling off." I asked her where this fear may have come from, has she ever fallen off before? No, she hadn't. So I coached her in the power of our thoughts, and how we look at things. I said "think about the fun you had, and how you were giggling and smiling when we first started trotting. If you think about and remember the good and positive experiences you have, it helps you look past your fear."
I often like to make analogies to experiences outside of riding that students can relate to; so, I had her think about when she first started to ride her bike on her own. "Remember when you had training wheels, and when you learned to ride without them and mom or dad held onto your bike seat? What did it feel like when you rode your bike for the first time on your own?" "It was fun!" she exclaimed. "And now you can ride your bike all on your own, like you've done it all your life!" "Yeah, you're right!" she said. I asked her to look at horseback riding in this same way, and her demeanor began to shift. She started smiling more and her posture changed, to show more confidence.
Half of being able to ride a horse is what is going on in your mind. I told her that I believe she can trot without holding on to the saddle, so she needs to believe she can do it too. If we tell ourselves we can't do it, then we won't grow. However, if we change our internal dialogue and what we tell ourselves, that we can do it, then we can begin to overcome our fears. Our thoughts become our reality.