Exercise and Condition
Retired horses need to be exercised each game month, just like your racing horses. They currently have two options for exercise: Turnout and Groundwork. Both Turnout and Groundwork are lockable options, with Groundwork having the larger improvement on condition. Neither options will use energy if it is the first exercise of the month, but Turnout must be done prior to Groundwork if you wish to use both. These are pretty straightforward and you don't have to pick jockeys or distances or anything like that. If you lock it, it will also work when you use your Train All button.
Like with racing horses, their condition will always be in gradual decline. You will have to do a more intense exercises now and then to keep condition boosted. Retired horses over 15 years old will also naturally lose condition more rapidly. Lower condition will decrease fertility and lead to higher risk pregnancies (see section on Pregnancy Risk). Thus, the peak time to breed is before a horse turns 15. This is a natural mechanism to encourage you to breed all/most of your mares every year rather than leaving massive amounts of them sitting around unbred for years on end.
The supplement, Get Fit, can also improve your bloodstock's condition. For more info on supplements see the Special Feeds section.