As far as I know the horses are gone, but I could be wrong. I believe two of those horses died fairly quickly after coming here. Caring for horses here is extremely difficult and expensive as there is no grazing and feed must be imported from the mainland. I believe that an 'exception' had been made in the case of those horses, but that generally horses are not allowed. Many people have chickens. Go visit Marina's store. They have chickens and guineas. You can get feed from Reimer's in Belize City. There have been goats and even pigs kept on the island at certain times of year for the purpose of slaughter.
Goats will eat anything; even tin cans. In the logging areas of Oregon, when the loggers are finished they bring in a heard of goats 'to clean up the trash.' They do a mighty fine job too.
Chickens and rabbits seem to do well here but I don't know about ducks or geese.
Pigs should do well but with the soil so sandy I don't know if they could be contained. Pigs are escape artists and can root out of anything but a deeply sunken strong fence. AND the smell is awful! I'm speaking from experience. My birthday gift for my 6th birthday was a little red pig with a curly tail.. I had to chase her everyday until we ate her.
I know the guy who had two horses had them taken away from him with the charge of animal cruelty based on the fact that the vegetation here was not sustainable.