If it is rare enough and you don’t have an emergency that is the right thing. Odds are the rest of your city doesn’t have the ability to deal with those temperatures and so you going out will make things harder for emergency workers who must get out. If your city deals with this often then everyone will know how to deal with it and expect you to deal with it. You cannot shutdown your life for something that happens every single year, but if it is just a day or two every 5 years it isn’t worth being knowing how to deal with it other than the minimum emergency needs (that is make sure your HVAC system at home can handle it)
In theory yes, but in practice no. Before we used fossil fuels (say 1000 years ago) the earth was on a slight cooling trend because a little organic matter still gets converted to coal. I can’t find the amount, but IIRC it was something like enough for -0.1C every thousand years. That number is so small that even a tiny amount of fuel use would keep us even.