When we first had our horses, we lived in a very urban part of Portland, Oregon. Fortunately, Portland is more enlightened than many smaller cities and towns and has no problem with livestock, as long as they are 50 feet from any house. We had 1/2 acre total, and the horses had a corral that was about 75 x 75, with supervised turnout on the entire back yard, so about 1/4 acre in total. With two horses, their corral was quickly nibbled down to the nubbins, but they were able to graze on the lawn.
What made this work was we regularly (every other day or so) walked them through our nearby city park, which comprised an entire dormant volcano. The size of their corral did allow them to run and play, so they never lacked for exercise or entertainment.
Full sized horses in L.A. live in smaller enclosures than what we had and are perfectly healthy. The key is making certain they are well-exercised, have appropriate shelter, and are never bored. It would be great if you had a friend's farm where they could occasionally go to run free.