J.S.
I'm not a very athletic type person, either. However, swimming and dancing are 2 things that I loved doing. If my high school had had a swim program, I would have been very involved in it!! I think once your daughter gets into the swimming or the horseback riding, she will realize how quickly that time goes. Horseback riding will also involve taking care of the horse after the ride ~ taking the saddle and tack off and brushing him down, etc. Depending on the facilities, your daughter will probably also learn how to saddle her own horse, and making sure the tack equipment is in good shape before she puts it on her horse (for her safety, as well as the horse's). There is far more to this class than "just" the riding.
A swim program is also going to involve the necessary stretching before the swimming, to minimize pulled muscles, etc. And, again, because there can only be so many students in the pool at any given "moment in time", your daughter will not be swimming all 120 minutes during those 2-hour classes.
Keep asking questions, both of the school district, the facilities, and your daughter, and you will come up with the right decision. I agree with the other mom....if your daughter already loves doing one of these, she just might turn out to be more "competitive" than you, or she, thought! But neither one of you will know until you at least try.