Saskia said "Really run the numbers though. I know a few people with small properties and if you only are keeping a horse or two it can be cheaper (once you put in extra feed, water, fencing, weed control) just paying to keep them somewhere nearby."
I think this is good advice, IMO 1/2 an acre for a horse is doable it would not be my first choice. You can also talk to your local 4h club or Pony Club they would have ideas and would be able to help you with Hay prices in your area. Having a barn with a good size stall plus fencing off a turnout area that will never have grass where you horse can be outside without being on the hole 1/2 acre. Then you can turn him out on grass for a few hours at a time to keep some grass.
Also, the amount of poop you are going to be cleaning up every day will really pile up fast, composting will go a long ways but composting isn't just letting the poop set in a pile, it needs turning to really compost well. Once it is composted you still have to do something with you composted pile of dirt.
If I was your parents I would look into boarding rather then trying to keep a horse on a half an acre.