The longer you let this fear grip you the worse it will get. It works that way with horses too. When you ride, request the lazy mare, and focus on keep your lower back loose. Have someone walk the horse so you don't pick up the reins. I have often observed a rider's back tightening the moment the reins are picked up. Spend the time focusing on letting your hips follow the rise and fall of the horse's hips. Start with you feet out of the stirrups which helps keep your knees relaxed. When you are tense it engages your body from heel to jaw and the horse feels this. Think Rag Doll. Do a couple of sessions like this two days in a row if you can as it will help you mentally. No trotting as this is to focus on you loosening up. When the big horse hastened away from the instructor I suspect you leaned forward and brought your heels back into his ribs cage to hang on. Keep in mind this has the tube of toothpaste effect. Squeeze like this and he will come out between your hands. As you learn to ride relaxed remember to keep your heels down. If you find you tighten in you knees when doing this, think Toes Up instead. Just changing the focus from heel to toes seems to work. That's what my students have told me.