Per the wiki:

At midnight on a horse’s birthday where it ages to 21 begins the possibility of your horse retiring. This means the last guaranteed full year of your horse’s life is at age 20.

At their 21 year age-up horses have a 10% chance of retiring with this increasing by 10% each age-up after. Any time between age-up to 21 to 29 horses may retire naturally. At age-up to 30, horses are automatically retired. Horses that have been custom-made will not begin to possibly retire until after their age-up on their 25th birthday.

It gives value and keeps it more realistic for horses to "retire" or pass away as they get older. Even if your horse retires right at twenty-one years old, that's one hundred forty-seven days. If horses never retired, the game would be overloaded with eternal horses, and nothing would have any value. 

You could always freeze horses you like the most? I have a freezer tab for some of my favorites I don't want to see go. You can also see them in the "retirement" tab.