Jasminegrays, is not just as straightforward as Yer or No. Does your neighbour own or rent the property? If rented, then one would need to know what Rules are set by the landlord / agent? If it was owned by the local Council the same would apply. Also, you would need to check with your Local Council if they have any rules set in place regarding such matters, however, they may simply view it as neighbour owning 'pets'. Are the animals well secured on the property or do they or can they enter unto yours? If the goat ate your washing off the line, or the chickens scratched up your flower beds, or any of the animals left poo on your property then that would only become a problem if the neighbour did not offer or make amends. If the animals were making unacceptable noise 24 hours a day, then the same rules would apply to them as the proverbal barking dog - one can call the council out to review the problem. But if all is in order and they are not making a 'problem' for people living round them, then most Law enforcing bodies would take the view of, live and let live! If the neighbour was charging kids for a ride on the pony or selling the hen's eggs, or goats milk, then one could ask the Local Rates Office, if infact they are paying Rates (in Nr Ireland it's still Rates - maybe yours is Council Tax?) however, my point is, are they paying at the Domestic Rate or the higher Bussiness Rates Level?
I know exactly your problem as we have a similar situation with one of our neighbours.
So the best of luck with your plight jasminegrays!