This actually isn’t that weird aside from the owner having contingencies on access to their animal. Sometimes owners need extra help with keeping their horses trained and exercised and that can be done with essentially leasing them out, but it is still your animal for however long the other party and you agree to. It keeps the horse in tiptop shape with training and exercise. It’s the parameters and wording that or a giant red flag from this lady. A lot of people will place their horse with another ranch/farm/family to ensure it gets adequate exercise and continued riding. It’s also a little weird that there’s no compromise on anything like even the farrier most individuals will compromise on something such as a farrier and a twice a year annual check up for the horse in exchange for keeping it exercised, consistently ridden, and the owner has access whenever as long as you know it’s scheduled. Definitely red flags but not an uncommon arrangement. Her arrangement is just missing A LOT.