Like in the original, keeping your citizens and buildings warm in is the top priority for success. Not only will warm citizens stay happier and refrain from overthrowing you, but they'll also be more productive and have a higher level of Hope.
Keeping my city warm in the original is the most annoying mechanic to keep track of, but as long as you understand how it works, you'll be okay.
Unlike the original game, you build your city in designated districts, and each district has its own heating needs.
It's one of their upkeep costs and some of the improvements and buildings you can construct require a certain level of heat in the area.
If you don't maintain this heat level, people have a higher chance of getting sick, no matter the district type. Sick citizens can't work, so make sure to keep them warm and happy to survive the frozen wasteland.