If you don't have a barn, a 3-sided loafing shed can suffice as protection from summer sun and flies and winter wind and storms. This means scrubbing tubs and buckets regularly. Groom horse often to remove dirt and stimulate the skin and coat. Horses are happier if they have company. If you own only one horse, perhaps a neighbor's horse can suffice, or a miniature donkey, goat, or even a chicken can be a barnyard companion.
Horses are creatures of habit, so stick to a routine.
Feed them at approximately the same times every day. If you must go away, employ the services of a dependable caretaker and leave the phone number of your veterinarian in case of an emergency. The veterinarian will ask you these vital signs when you call in an emergency. The temperature should then be taken, and any elevation over 101 degrees should trigger a call to your veterinarian. Pick out the hooves daily to remove stones and dirt and prevent thrush.