As you are around horses more, you will begin to ride horses with varying degrees of training. It is obvious and instructors are always hoping riders will learn and progress, then move on to different horses. Not bad horses, or dangerous ones – these are horses that are more sensitive. They may be a little more testy in their nature, trying to see what they can and cannot get away with. Horses that haven't been ridden as much will behave differently than the way a school horse would. These types of horses may also be a lot more sensitive to your cues. They might not even really know what the aids mean to them.
If you are advancing from a lesson horse, it is because your instructor thinks you are ready. This is great news and should help give you confidence in yourself and your abilities.
Since you are used to riding a horse that pretty much does as it is told to do, it will be a big change to ride a horse that requires you to be more assertive. This is not a bad thing! It is just one of the many lessons that we learn as we progress. These are all lessons that make us a better rider!
A horse that is a challenge for you should not scare you. You should not feel anxiety before your lesson about what he might do or how your ride might go.
A horse that is challenging for you is going to give you opportunities to learn a new skill and put the skills you already have to use. It will require you to be focused and listen to your instructor. That being said, this new horse that is challenging for you can't scare you to the point of making the fearful voices in your head override your instructor's direction.
If you really are scared, that is okay. Try to identify why you are afraid. Did the horse do something bad? Have you seen it act badly with someone else? Is it just bigger than the horses you are used to? There are many reasons you might be afraid of a horse, and that is okay. You should just determine what it is and communicate with your instructor. Confidence is hard to gain and easy to lose. As instructors, we would rather see you build more confidence and skills. That way, you will be more than ready when the time comes for you to again try that tougher horse.
There are other reasons beside fear that make it so a horse is too much for us. Sometimes a horse is too physically strong for us to handle. Horses with a tendency to buck, runoff or spook all the time are hard to learn on. Bad behavior is a challenge, yes, but you should never ride a horse you don't feel safe on.
There is no reason for you to ever ride a horse you don't feel safe on. Horses that buck, runoff, and spook constantly may be okay horses. They just may not be okay for you at this time.
It is never worth risking the chance of getting hurt. There is no shame in asserting yourself and saying you just don't feel comfortable. Riding should be fun and something you look forward to! Not something that you worry about or stress over.
Take your time, and learn on a horse that is appropriate for you. You have your whole life ahead of you to ride wild horses!