Just because the horse is outside grazing doesn't mean there is sufficient food. You may need to supplement with hay or pellets. Make sure the horse has shelter from the weather. A lean-to or overhang will help protect horses from sun, rain and wind. Check the fencing.
Horses have the uncanny ability to find anything to hurt themselves on.
Remove barbed wire from any fencing that horses come in contact with. Barbed wire can severely damage and even kill a horse if it tries to run through it or gets tangled up in it. Make sure there is plenty of high, dry ground during the rainy season. Horses standing in mud or water can damage their hooves and legs. Check the local county regulations about the number of horses you can keep per acre.