"Here's the problem: green wood won't burn."
Wood has been my sole source of heat for the last 12 years. I know that green wood doesn't burn.
But to get seasoned firewood, you have to plan ahead. Planning ahead STILL entails cutting down a tree. In a long-term, no-power situation, all the lower branches will have already been removed, and all the old buildings either demolished or are being lived in.
After all, in this kind of situation, I will not be the only one with the problem.