A green or "greenbroke" horse is one that is not yet fully trained and doesn't yet know its job. A green horse may know the basics of stop, go, and steer, but nothing more. Often, they have not yet learned to balance themselves correctly with a rider (or pull efficiently in harness).
In traditional hunting attire, a green horse has a green ribbon tied around its tail to warn other riders that it may act in a less predictable manner than a more experienced animal.
Sometimes show classes are limited to "Green" horses, although "Novice Horse" is a more formal term that is often used.