As far as I know, in Conil there are two "picaderos" that offer horse riding lessons and excursions on horseback. Unfortunately it`s not possible to ride horses on the beach during summer time, because it`s too crowded. But you`ll have an impressing view down from the cliffs in any case.
I just have experiences with one of the picaderos; the one that is close to Hotel Diufain (after this Hotel on the right, there is a small road leading to it) and according to a local from Conil "menos caro però menos professional" than Picadero Roche.
Unfortunately I found out, that it was not professional AND expensive. The horseback excursion is suitable for absolute beginners and costs 25 EUR for 1 hour. If horse riding is your hobby at home too, you won`t be satisfied just to walk a horse. Oh, they ride their horses "western-style", which I am not used too, but it`s easy to find out how it works.