The issue of safe and unsafe horses is touchy. horses are reactive animals and if you are nervous even the quietest horses will react. You should talk to the instructor and ride the same horse each lesson to build your confidence and learn how to cope and deal with the horse and understand the individual horses personality and how this horse thinks. You could also ask for lunge lessons for a while to get your ballance. Once you have ridden the same horse for a while and you feel confident with this horse then you can widen your horizons and try a different horse. This can take time but sticking to one horse at the beginning no matter how long it takes, its worth it. I teach children and adults to ride and they all have to learn about the individual horse, this is best acheived at first by riding and handling the same horse for a while. Happy horsingaround