Thanks, everyone, for your honest opinions. I think deep down I knew my answer should be an unquestionable NO on those horses staying. You helped me reaffirm it. It's very frustrating though...I have been trying to buy a house for three months and had two other offers not work out but for legitimate reasons. It's frustrating that these irresponsible, uncooperative people are standing between me and this house. But you are right, appeasing their crazy demands will only spell out more trouble down the road, and it's not worth it!!
I am still waiting to see their actual counter offer with the horse clause...if the seller won't stand down on the issue, my next course of action is to try and circumvent them and go straight to the bank. I'm not sure if that will work, but it's worth a try. I have a good solid offer for the approved short sale price. They would be crazy to allow the seller to refuse it because they are too irresponsible to rehome their horses. But, if it doesn't work, I'm prepared to walk away. I'll be disappointed, but better disappointed now than struggling with this for the next year plus.