Staying safe and healthy in bitter cold conditions isn't complicated. The key to dressing warmly lies in layering.
Still, just throwing on three sweaters is not the best way to go. You want to be comfortable, and if you get too warm, be able to adjust easily.
Here's an outline of how to dress for bitter weather:
Good old thermal underwear is a good first layer. Some people prefer silk, which feels better against the skin and is also a great insulator -- although it's a bit pricey. Silk also doesn't last as long as more rugged materials. Avoid 100% cotton, linen or wool on this layer -- they retain moisture which can lead to condensation and actually cool you down.
Time for something heavier; a knit sweater or sweatshirt works great for layer two. If you don't have a hood on your coat, a "hoodie" might be a good idea.
This is the coat. If you plan to be outside for any length of time, or if there's rain, snow sleet or hail, then a waterproof or water-resistant shell is an excellent choice.
A hood is a nice option, but a good wool cap is warmer. Since wool isn't water-resistant, the best choice of all is both the cap and the hood. A nice scarf, wrapped snugly around the neck, is a good idea, and it can be pulled up over your face for additional warmth if the wind is blowing. Gloves protect your fingers from frostbite, and make it much more comfortable when shoveling or brushing snow off of your car. When it comes to footwear, most people in Oklahoma don't own heavy winter boots, so consider an extra pair of socks and perhaps add some "no-skid" spikes, available at hardware and department stores. Women who need (or want) to wear a dress in the cold weather can always pull on an extra pair of pantyhose, and still look stylish while staying warm.