I keep my horse on 3/4 of an acre. Might be less, actually. She gets 24/7 turnout, as she has too much arthritis to be locked up in a stall. (As a side note, the practice of stalling horses at night to "rest" is rather outdated. Studies have shown that horses don't actually "sleep" at night, and continue to graze at night as they do during the day. They take catnaps during the day/night, and then get their 20min of REM sleep, and they're good to go".
I threw her into the pasture in August, and she was still pawing through the snow to get to the last of the grass in December.
I'm in the process of learning how to maximize grass growth for this year right now, but personally, I wouldn't think you'd have an issue keeping one horse on 3/4 of an acre. You'll have to divide the pasture and rotate, and keep up with manure, but it's do-able.
My friend down the road has 6 horses (one being a draft), and she has her horses on 24/7 turnout. They're always in a good grass turnout. And she has five acres. So yeah, with management, a small acreage can work just fine.