And she will never win, if you want to check there are thousands of cases about livestock inside the city limits.
Oh, I know, believe me. I had a long argument with my teenage daughter about this last summer; she wanted to buy some miniature Babydoll Southdown sheep and tried to persuade me that our ignorant suburban neighbors would think they were poodles, and I told her we wouldn't get away with this for long.
But this woman's case is a little different. This mini-horse is a service animal and her quarrel is with the apartment management, not with local government. If she drags out the Americans with Disabilities Act she might have a chance.
Speaking as a horseowner myself, though, I agree she'd do better to move to a place where the horse-ette could eat some grass. She probably doesn't have enough money to afford to rent a house, but farms often have a house or apartment for rent.