It sounds like you might be thinking about a different aspect of the game or a misunderstanding. Can you clarify what you mean by "putting your horse in the box"? Maybe you're referring to something else like:
* The Training Box: This is where you train your horse's skills. You won't get grease from training.
* The Breeding Box: This is where you breed your horses. You won't get grease from breeding either.
* The Stable: This is where you manage your horses. There's no way to get grease here.
Please tell me more about what you are trying to do in Howrse so I can help you understand!