Can you keep a horse on half an acre?

Well, it would be very cruel to keep a horse in a block that is very small. Horses usually love to run in freedom and not being locked up. It's just like humans, you can't sit in a confinded space for the rest of your life. You would like to at least get out and do something. I would say no, but its totally up to you. I would say the smallest paddock for a horse to be in would be 5 acres, no less.

Just one more thing, if you were to have a horse in half an acre, the grass in that very small paddock will be eaten by the horse within 24hrs to 36hrs.