As someone who has been burning wood for heat for 35 years, those people are out of their damn mind if they think 1 acre will supply them their fire wood. 1 acre will absolutely not grow enough wood to heat your home unless you are cutting it all down and moving away in a few years. It takes a decade of growth just to get a tree to the point where it is growing at a reasonable rate, it needs a root system built up before it can grow efficiently, and that root system is destroyed when you cut the tree down and the next set of trees needs to regrow it.
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.