Wow, that other list is way longer than I was going to give.
We (in southwestern PA) have had power outages, but never longer than a few hours in the winter. Other people around here have been out power for days at a time, maybe even weeks with the big storm last winter.
If you don't have/aren't allowed alternative heating in your apartment, you would likely need to find a shelter eventually. But with lots of heavy clothes, blankets, sharing body heat, etc you could probably tough it out for the short term. If you already have the heat on when the electricity goes out, your apartment will retain some of that heat for a while, and cool down slowly. So it would be several hours before you'd even need to start considering a shelter. Apartments are tricky. My grandmother probably could have gone 36+ hours on reserve heat from her building. Her particular apartment was such a heat magnet that she had her heat turned down and windows open all winter and was still roasting.
For short term winter outages, you'll need some sort of alternative lighting. I would go for long-lasting LED lights over candles for safety reasons. But you may want to keep a lighter and some candles in reserve. If you have a gas stove, and the electricity goes off but the gas stays on (what usually happens to us) you'll still be able to cook, just using a lighter to light the burner rather than the electrical auto lighter. Or even one of those wind-up flashlights. You might want to have a wind-up radio so you can know what's going on in the city, with regards to outages, street conditions and weather. Some packaged food that doesn't need to be heated, and a few jugs of water (though we've rarely lost water service).
You'll be fine though, I'm sure.
Winter driving can be hair-raising, but once you learn the ropes it's not so bad. It's really counter-intuitive:you can't slam on the brakes when you're slipping down a hill, and sometimes you have to hit the gas at just the right moment in order to keep going straight, or you'll spin out. When the roads are really bad, or if you're in a hilly area, you may not be able to come to a full stop without getting thoroughly stuck. You might want to find a nice empty parking lot and practice before you do a lot of driving around town. General rule, go slow, and pull over if you think you're going to lose control of the car. Better to be stuck on the side than in a crash.