case by case
I have a small dog who has been on at least 10 flights with me. She fits in a bag under the seat in front of me, and she has never once made a sound - much less caused a disturbance. I agree problem pets should not be in the cabin, but neither should loud screaming passengers. My point is that a rule shouldn't prevent the non-problematic pets from being able to travel. The noisy ones should simply go cargo, though I realize that requires some degree of responsibility and discretion on the owner's part.
On a separate note, I could not stop laughing about the horse, especially after reading the article and seeing that it wasn't a joke!