How can I convince my dad that i really do not want to learn how to ride a horse?

Personally I'd love it if someone was going to make me spend my summer riding a horse, but since you dont ... I think you should talk to him about why he is suddenly obsessed with filling your summer days with all these activities. Since you are twelve, I wonder if he is afraid that you'll spend your time chasing boys if he doesn't give you other things to think about. Some parents worry a lot about their little girls feeling that have to start acting older, and losing their childhoods. Ask your mom and grama if they will help you talk to your dad, and maybe agree on a compromise, where you get more say in what you do, and dont have to be so active. If you can find out what it is he's trying to prevent you from doing by giving you all these activities it might be easier to work this out. Maybe he'd be okay with you doing less as long as you were going to be in the company of an adult, and well-supervised. I think finding out what he's really worried about, and getting your mom and grama to help work out a compromise with him, are your best shot at a bit more freedom.