Our "off-grid" heating plan sounds a lot like Kazoo's. After not having a furnace for several days when it was below 10* outside in March 2013, we learned some valuable lessons. Fortunately, we could rely on still having gas and electric then.
Off grid? Isolate one small living space in your house to keep warm. Insulate it well with blankets, bed comforters, sleeping bags, plastic sheeting, whatever you have. We have a big buddy with several spare 20lb propane tanks, but that won't last forever and those aren't safe to use in a confined space. We could run a couple of 1500W electric heaters from our generator, but that also wouldn't last forever.
Assuming this is not a permanent condition, draining water pipes would be a wise decision to avoid freezing pipes and water damage. If we lost gas and electric at our house, without an expected return time and the long term forecast was significantly below freezing, we'd probably bug out.