I would then say it is a matter you would have to discuss with your yard owner. For example you could say something along the lines of you've not been satisified with the care your horse has been receiving and don't feel both sides of the contract have been upheld, therefore you wish to leave.
If the YO has not adhered to the terms of the contract then I can understand that anyone may feel they can deem the contract to be null and void. But be careful! If the YO chose to put up a fight you could find yourself in the small claims court. Two wrongs don't always make a right, sadly. Of course, you can always pay one month's "notice" livery but leave immediately - YO can't stop you doing that and it might be worth it for peace of mind.