If horse riding goes through your bloodlines, will you be a natural rider?

I don't think so. You may have a natural nack for it, but not because of your gene pool. Ones Chromozones are not based on learned traits of its parents, inherited traits (the once ped down through offspring) are things like natural instinct. You may have a good idea of how to ride because of how your parents explain it to you, or something along those lines. But learned traits are not ped down through X and Y chromozones, thus, not giving you a bloodline of those traits.