From my recent continuing education:

"The FHA and Section 504 do not exclude emotional support animals from their protections.
What does this mean?

It means that people with disabilities may request a reasonable accommodation to allow an emotional support animal to live with them even if their housing has restrictions or prohibitions on pets.

The issue then becomes whether the person with a disability needs the animal in order to have an equal opportunity to use and enjoy the housing or housing program. To make this argument, the person with a disability must make a request for a reasonable accommodation to the landlord, property manager or homeowners association (HOA) and provide the following information:

Indicate that you have a disability
Request that, as a reasonable accommodation of your disability, you are seeking to have an emotional support animal live with you
Describe the relationship between your disability and the assistance the animal provides

If you can show each of these three things, a housing provider or program must permit the animal to live with you unless it can demonstrate that allowing the animal would pose an undue financial or administrative burden or would fundamentally alter the nature of the housing or program."

Though the wording indicates a landlord can attempt to demonstrate that allowing the animal poses undue financial or administrative burden, there was not a successful appeal to date.
Examples included: different types of pigs, a small pony (yes, living inside), rabbits, mice, rats, and snakes.
I did not think at the time to ask if wild or exotic animals prohibited by the Department of Wildlife might be allowed with a permit.

Interesting