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.
Knew an attorney that took a pony case using that line, thing drug on for about three years and in the end he lost. You just cannot defeat zoning laws. The only people that have livestock inside the city limits on the east coast are grandfathered farms. On the west coast you have green belt zoning. As well as grandfather land.