A Virtual Horse

Overpopulation & Overbreeding

On these topics:

A breeding change has been implemented. Now only level 5 horses and above will be eligible for breeding.

Some other overpopulation issues will be resolved when a retirement age and location is set into the game. There is still time however before the oldest horse in the game reaches a retirement age, but this addition will be coming. For now it is best to worry about your own horses and not all the horses in the game.

Overbreeding is a bit of a personal perception and preference.
You can avoid overbred horses by choosing to purchase or breed the ones that are in your opinion not overbred if this is an issue for you.