On Account settings, players have a button that allows them to "Freeze" their account. Once the account is frozen, horses won't age, and if you groom them, they will stay clean.

they can also be frozen in a tab, if you go through estate -> manage -> tabs then you can make tabs and freeze them

It could be possible the horses for sale/frozen the owner got busy irl and simply froze everything over and hasn't come back yet.