I keep my horses on 5 acres. It is difficult in Illinois to find a split farm with that much. Many people buy an old farmhouse with about 2 acres adjacent to it. I know of one owner who keeps 5 horses on that. I have a friend who keeps her 2 horses on 6 acres.
I looked for 12 years to find what I wanted:
--some kind of fencing there already
There were several places that almost worked, but I would have been difficult. One had 2 acres on the corner of 2 country roads, a nicely finished horse barn and turnout, but the really pretty house was really pretty small with 2 bedrooms, and just wouldn't work for the (then) 5 of us.
I spent 14 years boarding. The farmer (owner) kept diminishing areas for me to ride in, and I spent too much time crossing a really busy 2-lane highway--we used to call it the "SR150 Motor Speedway"--and rode ditches next to farm fields. I HATED it. There was trash in the ditches and sometimes drivers would play "chicken" and see how close they could drive next to your horse.
With 1/2 acre your schooling abilities are going to be pretty small. I grew up in a suburban housing development and we had 1/2 acre. We could play baseball in the back yard...but that's about all.