The retirement home is owned by a non-player character named Gisela. She owns the retirement homes in all continents, and you can retire horses regardless of what continent you are currently on.
Gisela provides a loving home for unwanted and old horses, which is why you won't receive money upon leaving a horse here. Despite its name, the retirement home is a place for all unwanted horses regardless of their age. You can even retire foals. Once you retire a horse, it permanently transfers into Gisela's ownership. You won't be able to retrieve the horse, so double-check before clicking!
Retiring a pregnant mare causes her pregnancy to get terminated, so that no foal will be born. When you retire a foal under 6 months of age, it continues to display next to its dam until weaned. Once it turns 6 months old, the foal automatically leaves your stables and shows up in the retirement home. If you retire a mare that has a foal under 6 months at her side, the foal will stay next to the mare at first. However, the foal automatically returns to your stables once it reaches 6 months of age.