Old age? - Are they worth keeping?

When a horse hits old age and its not particularly well bred (starters mostly) is there any use in keeping them into old age? Since the price of a new box keeps getting steeper, is there anything you can do with the older horses that makes it worth keeping them?

there's a quest to keep a couple til death, i don't have the details. might as well do it with cheap quality ones, better quality you might want to sell at a younger age while someone still wants them