For winter:
Snow tires: All Season tire are really only 3 season tires. Below 7 C (44.6 F) so called All Seasons quickly lose traction due to the fact the rubber compound isn't soft enough. Winter tires are softer and contain silica. Their tread is also deeper and more aggressive. They are mandatory in most provinces in Canada and northern states
Fully charged battery: A weak or dead battery will freeze in extremely cold temperatures.
Synthetic Oil: Highly recommended. Stays fluid at low temperature making engine easier to start. Car warms up quicker I find because the engine heat isn't wasted thawing the dino oil.
Full tank of gas: Running out of gas at -20C isn't fun.
Survival mentality: Having all the essentials to avoid problems such as jumper cables, traction aids, shovel, flashlight, fully charged cell phone, blankets and warm clothing. Be mindful of the weather. In winter the conditions can change very fast.
Good driving technique: Pretty much self explanatory.
Good tire inflation: Add a few extra PSI to compensate for temperature drop. Inflate when ambient temperatures are above freezing. Inflating tire below freezing could result in a flat tire because the valve freezes open.