We lived in Iowa for 10 years..... we did usually have a couple of blankets in the car when we travelled, but not otherwise.... I remember my brother made up a mixture of cheap cat litter and sno-melt, and kept that in the trunk... the extra weight helped in the trunk for traction on ice, and if you DID get stuck, the cat litter helped provide traction, and the sno-melt helped melt the ice.
Some people suggested keeping a candle and a coffee can in the car... a candle can do amazing things to warm an enclosed area, if necessary, and the coffee can can be filled with water, and melt the snow over the candle.
Supplies you should always have around the house would include:
Batteries, candles, matches, flashlights, food that doesn't require preparation, stuff like that. A battery-operated radio comes in handy, also.
Propane coleman lanterns are handy.... they put out a wonderful glow! Just be careful burning anything in an enclosed area... carbon monoxide can build up if you aren't careful.
Most of this you probably have around the house, anyway.
If the power goes out, just bundle up the kids in layers..... (our power went out Thanksgiving day in 1991... and my son was only about 10 days old! That was fun... but fortunately, it was only out for a few hours.... we put the turkey on the smoker to keep it warm until we could finish cooking it.)
In the 10 years we lived there, I don't think we went more than 12 hours or so without electricity...... and this was in a very small town! (State Center)