The most important thing to purchase is an artificial orb, or globe, to light up your room during the 6-month-long winters. As the sun rarely makes an appearance, you need something to tell you when it's daytime and keep you from getting depressed. (Another remedy is to buy a clock that tells jokes.) In winter, living in Ann Arbor is analogous to living in a cave, only the cave is very big and you can drive around.
The cold in the wintertime is dangerous, so it's best to stay inside. If you must venture out, wear two or three coats and put heated bricks in all the pockets. You can make your own heated bricks with regular bricks: just heat them in boiling water for five minutes and put them in your pockets with tongs. They'll help keep you warm, and the extra weight is good for traction. Note: don't warm the bricks in the microwave; they explode.
Finally, if you don't have a pair you'll need to get some snowshoes. Last winter a few students tried to walk to school in regular snow boots and sank in the ten-foot snow like it was quicksand. Fortunately there were other students on hand to fish them out. (They tied backpacks together and made a sort of rope.)