Different cities, townships, counties, etc. are going to vary a lot in what is required in this sort of situation so I can only tell you what I know based on the city we live in, so where they live could be very different..
If their local ordinances do not allow horses on lots less than five acres they probably should have gone to their city or township and applied for and been approved for a conditional use permit prior to getting the mini. Our city is pretty tough on people that do not follow city bylaws or ordinances whether it is building a fence too high, or building an addition that exceeds their hardcover restrictions. for example, we are allowed two dogs and if you have three you have to apply for and be approved for a kennel license. If you don't do that, and it comes to the cities attention you risk being fined and being denied the kennel license and being told that you have to get rid of one dog. If you ignore that, it is up to the city how hard they will push whether it is more fines or actually getting a court order.
Most cities are too busy to go out looking for people that are not following local ordinances and the fact that these peole were sent a certified letter probably means that a neighbor that doesn't like having the mini in the neighborhood complained to the city and now the city is following up and enforcing local laws.
What happens next will depend on how restrictive the city they live in is and how flexible they are willing to be. Applying for something like a conditional use permit involves going through the normal channel and either is denied or goes on to the city council where they review it and then vote for or against allowing the permit. The vote happens at a city council meeting which is open to the public and anyone that wants to can come to the meeting and speak their mind for or against whatever is on the agenda for that meeting, including something like this. I think they would need to have a valid "hardship" reason for the permit and also address concerns about manure removal, shelter, fencing, flies, noises. etc, and they probably will need to find several neighbors that support them and are willing to attend the meeting and speak up for them. It also means any neighbors opposed to it can speak up as well.
I hope it all works out for them but they really need to get down to their city and find out exactly what they need to do asap. Unfortunately, just talking about how much they love the mini or how good he is for the kids and the mom with alzheimers will not be enough at this point. They will need to address the rules and restrictions and concerns of the neighbors and not let emotions come into play. Getting the horse certified as a therapy animal at this point probably will be helpful, but going through that process also takes a while and doing it now after they got the letter from the city may make it less helpful and it probably will carry less weight than if they had already done it a year ago when they got the mini.
I am probably not sounding very encouraging, but my husband was on our city council for eight years and I am being realistic. They (the city) see and hear just about everything you could imagine from people wanting exceptions to be made or a permit to be granted and they just want people to do their homework, know the local ordinances/laws. Ignorance of local laws is not a good defense for not following them -- ever been stopped for speeding and gotten out of the ticket by saying you didn't know what the speed limit was on that road?. Anyone wanting an exception to be made needs to present a clear, concise, well-thought out plan and be prepared to address any and all concerns the city or neighbors may have and present a convincing, well-thought out argument.
This topic and similar situations have come up here on the forum several times over the years so if you use the search mode you can probably read through those older posts and you may get some other helpful ideas from those other experiences. Some have worked out happily and others unfortunately did not.
