There are two places where you can learn to ride, years ago you used to get lessons where the equestrian federation is now near raayan. this is where the race track is. The other place is Al Shahib Stables ( dont think thats the correct spelling) its near Qatar Academy, and Qatar Foundation.

I am sure there are more places - check out the Marhaba Magazine, it has a section in there on things to do in Qatar and I think they list horse riding.

 

Think Aspire is just for the students that attend Aspire, I go up there everyday for my exercise I have yet to see a horse on the sand track they have up there, although I did see one horse in a temporary stable set up there.