You have gotten some very good ideas from others. I'll add that horses are very active at night if you allow them to be out. They don't sleep eight hours in a row like humans. They have very good night vision. Horses are saner and healthier if allowed room to move 24/7. Movement is necessary for their digestive tract to work properly.
Can you create a paddock (smaller area that the horse(s) will eventually strip of grass) with the run in? A dry lot will allow you to close off the pasture if you need to, but allow the horse to move in a larger area than a stall. A paddock can be used for double duty, such as a round pen or riding ring. You will have to pick up the manure before riding.
Link below is a 'thinking outside of the box' site that is an alternative to pastures. It is based upom the movements and culture of wild horses. While life-time equestrains may poo-poo the idea, I believe it has merit. It works for smaller acreages to create movement. Slow Feeding Horses on Paddock Paradise Tracks - Paddock Paradise Wiki
Keep asking questions, and work with an instructor or trainer before your purchase. You might contact your County Extension office about pasture management in your area. I say might, because some county Extension services are very knowledgeable about agriculture, but not about equestrian issues.
Have you worked on a monthly budget for the horse? That in itself would be a good question to post.