Rules for cats are often very different than rules for other kinds of animals.
Turkeys would would be poultry, and guineas would probably be considered poultry as well. Poultry are sometimes considered livestock and sometimes have separate rules of their own.
But if you did check, and they do...
If the forest is not private property, then who DOES it belong to?
The government of the country? The state? A local Homeowner's Association? A big corporation or company? It sounds like you are in the USA, where every piece of property belongs to someone, even if that someone is not a private...