I'm sure this has been brought up before. But I have always wondered how can I "lose my access to horses" when, the last time I checked, I still have plenty of horses in the field. I know this is done for gameplay purposes, but it is kind of silly when you think about it.
Horses do not expire so the way to lose them is if they were in a trade and it is not renewed or cancled. If it is in your domain, then the road is cut, or harbor or what ever access brings it to your civ. Lose your capitol. I am not sure about having enemy troops sit on your resource, but I think that will stop them as well.