It's easy. Make sure you have a block heater or remote start if you want "comfort", otherwise make sure your hands are dry before grabbing the steering wheel, lest your hands freeze to it.
Get used to scraping ice/frost from all exterior surfaces (car, pavement, keys, glasses, hat, shoes, etc) and you will be fine. Remember layered clothing!
--ETA: Good tires are all you need. I can get around 364 days out of the year with a 4 door GM car. Front wheel drive is all. That other day of the year is when moving it would hicenter it. They are good with clearing the roads if you move to a town > 20,000 people (I am in Sioux Falls). Studs/chains aren't needed unless you are in the country, and then aren't legal/needed on the interstate and major highways in the East part. In the Black Hills, that is different, a front wheel drive car wouldn't get you around well if you lived in Sturgis.
Culture shocks: Most everybody will be speaking English, you need to drive 75mph on the interstate, gas heat is most common, with a room sized kerosene heater for backup. Keep candles and LED flashlights around, dark is long here, compared to lower latitudes (like TX/CA/SC/FL). In nicer parts of Sioux Falls and many smaller towns, you can leave your house unlocked without a worry, and in many places outside Sioux Falls and Rapid City, even your car!
Good boots are a must. About 3 pair. 1 pair of steel toe leather with no insulation, 1 pair leather with light to medium insulation (these first two pair will get you around to/from work around town, etc, and will be used the most. I like Dr Martens for the 1st pair, and Danners for the 2nd). 3rd pair is heavy insulation full waterproof so you can walk through 3" of slush and stay dry. That is for digging your car / house out, hunting, being outdoors more than an hour doing light work with your feet surrounded by snow/slush.
Gloves are also something to get in several thicknesses. the 10-40 degree weather ones, the -10 to 10 degree or moderate windchill ones, and the sub -10/high windchill ones. again, the 10-40 is the most used, but if that is all you have, you will be frozen after spending an hour outside at -18 with -85 windchill.
Scarf or an ATF® Approved Backlava to cover your nose/mouth/neck in the wind. This is a "must have" if you will be outside more than 10 minutes on a "bad day".
Here are some guideline averages/extremes from historical data:
Temperatures:
Snowfall: (This is average, remember, we didn't get any significant snow until about last week! (12/1/05)