And any external hallways and stairwells, also. If you can pull your mattress into the front room or dining room (whichever one is large enough and central enough to the kitchen and bathroom), do that, or plan on sleeping on a couch or on pillows.
Get a bunch of emergency candles and tea candles. Not the Yankee Candle type, scented candles put off gasses that can cause health issues.
Candle tapers are good for lighting, but not so much for radiant heat unless you have a fire-place mocked up to put dozens in and sit in front of. (hmmm, a cardboard and foil emergency fire place?)
Tea candles can provide a "pre-heat source" for blankets - if you put them in wide bowls, with some punched foil or a trivet/cooling rack over the opening and carefully move the blanket over to catch the heat. (I've done this with socks and blankets camping out at SCA events)
You can also create short term radiant heat with tea candles and aluminum foil if need be, but remember - candles must never be left unattended.
If you're going to have to sleep on the floor, you need to be off the floor, or be sleeping on layers (pillows, cushions, and a quilt underneath you). The layers under you will keep you warmer than the layers over you.
Tack up towels around the doorframes to those closed off rooms and window frames, and vent systems to cut down on draft. Keep your dogs in the same room you will be staying in if the power goes out. Bring all the things that you will need for a week into the bathroom or main room.
Remember to layer, layer, layer. If you cut down on the drafts, layer, and narrow your living into two/three rooms, you should be able to survive a few days with no power in sub-freezing weather.
Also, get a couple gallons of water in pots standing by for water/pipe emergencies.
Another primary issue would be keeping your phone charged when the power goes out, because you will need communication for emergencies. You can get extra USB power packs if you need to at most hardware or department type stores.
Basically, if you don't have a space heater that doesn't depend on electricity, you're going to have to go with layers and body heat, and work on cutting down as much draft as possible.
I remember my grandfather talking about surviving winters in Lancaster County, PA once the firewood ran out when he was a kid (middle of 10) living in a rickety wooden house with stone foundation. They brought the animals in, and all slept on quilts bundled in the front, and put grease-coated rushes in the fireplace to smolder and keep heat going until they were between storms and it thawed out enough his father and uncles could cut some more firewood.
I don't know how you're going to be able to help your downstairs renter; if y'all are comfortable enough with each other, your renter might need to come upstairs and stay with you and the critters in case of a power outage, unless s/he has a place already set up to stay.
Just be prepared to give him/her a discount for any time that the apartment is too cold to live in; that's only fair.
Good luck, and hope your power doesn't go out.
ON EDIT - SAFETY ALERT ON INDOOR HEAT SOURCES! Never run natural gas, sterno, propane, kerosene, bio-fuel, or even clustered candles in a moderately sealed room without some sort of overhead vent nearby. E Asphyxiation is a serious problem, and people have died of CO2 poisoning during the winter trying to heat their house with their gas ovens or camping stoves without working ventilation.
You cannot "smell" CO2, and you will not notice anything but a mild headache or drowsiness before it's too late.
Haele
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It also has a little orange car with orange skid marks that flashes. I didn't notice that until I was almost in my driveway and only slid a little bit so I actually noticed it. 
