Don't forget the free fishing rod/equipment.
Of course it depends on the land and the house. But here's some Reddit comments also estimating the need at < 1 acre
https://www.reddit.com/r/homestead/comments/1jnpbug/how_much...
And even with a well managed rotating stock of trees, you are going to at best get just over half a cord per acre. And in my area which is as close to the same weather as Northern New York as it gets, I would expect they would need atleast full 3 cords of wood to make it through a mild winter, more if it is a colder winter or if no snow builds up to help insulate or if you live on an open plot where wind can blow over your house.
I wouldn't even consider trying to survive on my own tree wood unless I had at least 10 acres to harvest off of, and it would still depend on the type of trees growing there and is still kind of straddling the edge of sustainable long term.
Maybe if you went full 16th century and started coppicing the woods and maintaining bare minimum heating you could do better, but coppiced woods also takes a decade to initial establish and maintain and nobody has coppiced woods just sitting around waiting to be utilized.