We don’t know anything except what the OP has told us. Which isn’t much. What we do know is that the horse WAS turned out, just not where the OP wanted the horse turned out. To me, that is not enough to warrant all this if the BO isn’t doing her job tough crap, crap.
Grass is hard to come by in the OP’s area? Why do we think it’s positively criminal that a horse that will tear up the grass isn’t turned out on the grass?
Was the OP looking for another barn when December 1st rolled around? From what has been posted, it seems that the only reason she didn’t give notice on the 1st is that she hadn’t found another barn on the 1st.
That’s not good enough reason not to give proper notice, contract or no contract.