Same, upstate NY as a teenager. A couple cords stacked a few yards from the house, enough for the entire year. One problem we would never have is heat, except that if the power went out then some rooms would go cold with no way to run fans to move the air around. But no one would freeze because most of the house could be like a dry sauna.

I think in this case it must be more about a level of poverty so extreme they can't even pull together the years supply ahead of time, even if the community as a whole does have it all ready.

Maybe they don't distribute it except it tiny amounts for some reason? Maybe it gets stolen or sold?

I mean I can only assume that there is some reason they can't do the sensible thing. I couldn't imagine risking relying on daily or weekly deliveries of tiny armloads of wood. I can only assume anyone doing that has no choice or at least thinks they have no choice. I'm sure there are a few individuals who are just, let's say thoughtless, because there are always some, I'm not counting those.