Is this legal to do to our horses?

Sounds like the stable owner is not a very reasonable person, and certainly not willing to negotiate or come to an agreement. I would try one last time to figure out a mutually acceptable compromise, and then I think you may want to seek the help of an attorney. Someone experienced in contractual law. I find some of the things the boarding stable owner did odd, including not giving you a copy of the contract. Also, I don't think they are able to hold your property against your wishes, if you have paid the bill in advance. I think the law might be a little different considering the property is a live animal, not just a piece of inert property.