It is not a bad thing to think about bugging in and what you need to do to be prepared for it. I think that is the whole point of emergency preparedness for homeowners.

Well, furniture won't provide a lot of firewood.
Not only is it usually made out of other stuff instead of wood, but even wooden furniture does not make much of a pile of wood once it is broken down.
Then you need to deal with having a fireplace or stove to burn it in. You would be better scavenging from dumpsters and construction sites for wood it you were going to do that.
Cooking will likely be outside with a barbecue pit or can stove simply because you likely don't have a fireplace in your house, but if you do have a fireplace or wood stove it suddenly becomes a useful feature instead of just an architectural ornament.
Straw (dead grass) can be a useful cooking fuel. Chinese peasants have relied on it for thousands of years.

Consider oil lamps, slush lamps, or candles for heat and light.
If it is cold you will be wearing more than just one sweater too.
Most houses can be managed to stay fairly warm, opening drapes in the daytime and closing them at night to trap heat from the sun, that sort of thing. Anything that adds insulation is good.
If you are forced to gather water and need to filter it cheaply you might want to try slow sand filters (bio-sand filters) because they are cheap to make and 5 gallon pail version should deliver about a liter an hour.

Food will likely be scavenged in your scenario. You won't have time to grow a garden if it is not already being grown. You better understand urban/suburban trapping and the raising of domestic meat sources too. (rabbits, pigeons, squirrels, possibly ducks and geese, maybe even rats if it gets to the starvation point.)



Your basic proposal pretty much suggests Paris under German occupation in WWII or Berlin when they were isolated from the west right by the Russians at the end of WWII. ( Berlin airlift,not East Berlin after the wall so much)