Outdoor survivalist here, slept outside without a tent in 40 below
winter weather.

Do you have outdoor sleeping bags?  If not, the best thing to do is
build your own "cocoon" out of as many layers of cloth as you can find.
Sheets, blankets, even towels, make yourself a nest and sleep in that.

Clothing:  Again, layers is the key.  A sweater will not keep you as
warm as a sweater over a turtleneck over 2 t-shirts.  Wear a hat, even
to bed--you lose body heat through your head.  One note on this:  If
you find yourself sweating, take a layer off.  If you sweat, then the
sweat will cool at night and chill you.

Heat Sources:  If you have any heat sources, like a grill or camp
stove, hang tarps around an area to keep the heat in, and sleep there.
I did this once...caught outside in snow, we got into a cabin, put
tarps up all around the kitchen area, turned on the stove, and used
that as a heat source.  The tarps stopped the heat from escaping into
the rest of the cabin.

Be extremely careful with open flame indoors.  Don't fall asleep with a
camp stove still on.  Let it warm up the room, then turn it off before
you go to bed.

Good luck,

--Fil

Some people did bug out. I heard of some folks who left their home
about the time the trees came down -- glad to be out, the roads were
blocked for days.

So far, no one has mentioned a generator to power the furnace. I'm a
bit surprised.

If you won't be able to wrap up enough to be sure of avoiding
hypothermia while you sleep, go to a hotel, or to the home of someone
with a backup heat source, instead of taking a chance at freezing to
death in your sleep.