Minis don’t need a lot of space as a big horse does. If you have a large backyard and a small building or shed for shelter that should be sufficient. They like to be outdoors as much as possible. Please provide some sort of shelter for them with at least 3 sides to ward off the cold, wet weather. In the summer, they like to find some shade to get under also. If you have a barn to stall them, please turn them outside everyday for exercise. You will also need to keep the manure picked up and some sort of bedding, such as shavings or straw, which should be changed at least weekly.
This information is based on my knowledge of what I know from being around horses my entire life. It is a guideline, but please contact your veterinarian regarding the care and health problems of your miniature horse.