For all practical purposes it seems you've got yourself a free tree stand. BUT, imo it doesn't belong to you. You have simply taken into your posession somebody elses property and it would be extremely difficult if not impossible for them to get it back. But it's not yours. Because you found it on your property doesn't mean that it automatically belongs to you. If someone has a car accident and their car slides off the road and on to your property does the car automatically now belong to you? Of course not.

Now you asked "Do I have to give it back?". IMO you don't have to. I doubt there's anything the fellow would do to try and make you return it but I do think that would be the right thing to do. Certainly he's guilty of tresspassing but I don't think you are the one to extract the fine. The right thing to do is what some others said. Turn it in to the police and let them handle it.