I *think* from case law that when a notice period is stated for one party and not for another, the notice period is assumed to be the same for both parties (whatever is stated in your contract as owner's notice period.)
As quirky. If she does follow through and tries to take you to court then countersue for loss of earnings, costs relating to lessons and keep of horse as well as emotional distress.
In fact I would be tempted to inform her that you will do this if sued, that you are not a naturally litigious person but if pushed will become so.
By the way most household insurance covers legal costs for the occupants.