It depends on how long/ hard you ride, just like every other work out. Personally, I believe that to be in optimal shape, riding should be paired with running, swimming, or at least one other activity which works different muscles.
bsms, how long/ hard did you run before? If you were an avid runner, that's probably why riding isn't aerobic for you. For me, it's aerobic because I don't do other aerobics.
Whether riding is a work out for you depends on what shape you're in. Although I do think it's an exercise, it's not the best out there if you really want to be in shape. from 1-10, I would give riding around a 5 as a work out, and by this I mean riding for at least an hour for 4 or 5 days a week.
Although my legs are pretty muscular, my brother can run way longer than me because he's a rugby player. My dad is much stronger than me because he does a lot of strength training. If I put them on a horse, they'd die from the exertion because they don't really use the muscles that I do, just like if you asked me to do my dad's work out, or to play a rugby game, I couldn't do it either.