You will always need snow tires in the winter.
Normal tires are made of hard rubber. Tires sold in the southern US are made from still harder rubber. Hard rubber lasts a ton longer than softer rubber - but - hard rubber will get you killed in winter driving around snow and ice. In winter you want soft tires that will grip the road like Blizzaks or clones of them. You can also have snow tires 'sipped' here cuts are made in the threads to let them grip more.
I live in Alaska. Just south of Fairbanks in the interior. My 4x4 big F-250 has studded snow tires and 1,000lb of sand bags in the bed. It will go anywhere, anytime, no matter what ice or snow storm is happening. However I don't drive that thing much at all due to the lousy gas mileage - my daily commute vehicle has 4 non-studded Blizzak tires and three 100lb lead ingots in the back. Even with 2 wheel drive you want 4 snow tires. The ones in the back with extra weight get you moving. The ones in the front with the engine weight are what allow you to turn and brake.
Consider this. Your snow tires need to be thin. This lets them toss snow out of the way, dig down, and get traction on the road. Wide tires will make your vehicle sit on top of the snow and just spin! On both the truck and car I went with the tallest, skinniest tires that would fit with no trouble. These will also be the most affordable ones since wider is usually more expansive.
Pay attention to your rims. If your car has nice lightweight rims for better gas mileage - you don't want to run them in the winter. Here, buying a cheapo-set of heavy steel rims is what you want - they will take the beating is you slide into a curb. The added weight is helpful. And having summer tires on pretty rims and winter tires on heavy ugly ones - you will be able to swap them all by yourself and not have to wait half day to have them mounted and balanced every fall and spring.
If you decide to put weight in the back - I suggest buying bags of sand or pea gravel - this way if you do get stuck.... you have plenty of sand and some gravel handy to get you unstuck!!