Your dad might just be lashing out right now too. Not saying it's the right thing to do, but his feelings are probably hurt that you don't want to live with him. Maybe if he calms down he will change his mind. Hope everything works out.
Sorry you are having such a difficult time. Maybe your mom could pay 1/2 and she could talk to your dad about paying the other 1/2. Or maybe she could tell him that she will take the amount of Jacks boarding of the child support agreement. IMO, I think you should talk to both of them about how important Jack is to you and how hurtful the situation is to you as well. Good luck sweety, I know how difficult it is being stuck between parents who aren't being as adult for you as they should be.
I agree with MN Tigerstripes about your dad. His feelings are hurt right now. My mom and dad were like that years ago (back in the "80's) when they were getting a divorce. My daughter's father was like that when we got a divorce. But he calmed down, realized what he was doing to her, and tried buying her everything she wanted. Trying to get her to move in with him of course. Hopefully your dad will come around. I do believe you need to talk to him calmly and rationally and tell him how you feel. I know how easy it is for a discussion like this to get out of hand really quickly, and for tempers to flare. If he starts getting upset and raising his voice, don't raise yours to match...that'll just make things worse. Just calmly tell him that that's the way you feel and get up and walk away. Give him some time to digest everything. It may help. If you're considering leasing though, and your dad does come around to at least pay half, consider a half lease. That way, you'll still have access to him.
I'll keep you in my thoughts and prayers. Good Luck!
I think there are some good pieces of advice on here, and I'm sorry you're going through such a rough time with your family right now. Maybe you could sit down with your dad and explain that you know this is between him and your mom, but that him forcing you to give up your horse makes it feel like you're the one who is being punished. He might be too hurt and angry right now to see that he is really hurting you too. If that doesn't go over too well, then I suggest looking into a lease.
It takes a lot of courage to talk to your parents like an adult. I had to do a lot of reminding to my mom that I was the child and she was the adult, it was always hard to be in the position but ultimately your parents can be pretty amazing when you approach them calmly and rationally. Good luck to you, I'm so sorry you're facing losing your horse while also going through your parents splitting up. I hope you have some trusted people in your life that you can talk to about all this.