I've lived in Michigan for 7 years and in places where it snows almost all of my life.
1st advice is layers. Have a closet with long underwear, thicker yoga pants, fleeces, sweaters, flannels, wool socks, and sweatshirts to wear under your winter coat.
Down jackets are a safe bet for staying warm, but there are other winter options too. Leather with a nice thick interior works well, and there are plenty of snow jackets in stores up north.
Check the tires on her car. You should switch to all-season tires, and if you're in a rural area or somewhere that doesn't get plowed often, consider winter tires. You don't need 4 wheel drive unless you'll be driving off-road in the winter.
At home, thick pajama pants, blankets, and slippers all make the cold floor more comfortable in the morning. Heating is generally cheaper than AC, so use the thermostat. Also consider a foam insert to slide under the doors and prevent drafts. Most newer buildings are well-insulated, but older houses may have gaps in the doors and windows.
Take a Vitamin D supplement in the winter, since we don't get a lot of sun.
Hats, scarves, and earmuffs are all good in different ways. Try each one of them.
Make sure the gloves you get are waterproof. Cloth gloves don't help when you're cleaning off your car.
Speaking of, buy an ice scraper and brush combo and always leave it in the car, even in the summer. Also leave a blanket in the trunk. It's useful.
Learn to ice skate. It's a lot of fun and a good place to make friends.