There has been little research done on the space requirements of horses. If you are attempting to figure the carrying capacity of land for a horse, then a good rule of thumb is 1-1/2 to 2 acres of open intensely managed land per horse. Two acres, if managed properly, should provide adequate forage in the form of pasture and/or hay ground. But this is highly variable depending on location.
If you are depending on the land for exercise rather than nutritional needs (i.e., your horse gets hay each day), a smaller area may be adequate. Also be sure to check your state and county agricultural statutes since different states have different minimum land requirements for livestock.
In the Eastern regions of the country on properly managed pasture, 2 acres will support the forage needs of a horse.
In the Southern region of the country on properly managed and in some locations irrigated pasture, 2-10 acres will support the forage needs of a horse.
In the Midwest region of the country on properly managed and in some locations irrigated pasture, 2-10 acres will support the forage needs of a horse.
In the West region of the country on properly managed and in most locations irrigated pasture, 2-10 acres will support the forage needs of a horse.
With non-irrigated dryland pastures, you may need up to 30-38 acres per horse to meet its total forage needs.
One acre is 43,560 square feet or approximately 210 feet x 210 feet. Obviously, many people keep horses on smaller amounts of land and do not depend on the land to provide any forage.
The minimum area needed to house a horse for turnout is 0.1 (one-tenth) of an acre, approximately 4,500 square feet or 75 feet x 60 feet for an exercise lot.
