The key to dressing for your winter runs is LAYERING UP.
Base Layer: This is the most important as it wicks the moisture away from your body. Manufacturers like Craft, Mizuno, Kari Traa, Smartwool make great base layers for moving moisture.
Middle Layer: This is the layer that will create warmth. Apparel with a slightly fleeced backing will trap the warm air that you generate while you're running. (Some tights will incorporate these properties along with those of the outer layer.)
Outer Layer: Your top layer will block the wind and help you retain heat. With deep chills, you can go pretty heavy, but something that has wind-blocking properties is essential.
Socks: Make sure you don't wear too heavy a sock, as you will restrict the blood flow in your feet and actually feel colder! Merino wool found in Darn Tough, Smartwool and some Feetures socks is awesome! And, if you want to add a little warmth to your legs, get a sock that goes up higher, such as a crew-style sock.
Shoes: If you want to add a little warmth to your shoes, you can add som duct tape over the top mesh once you've laced up. This will help create a barrier to keep the cold air out.
Hands: Mittens are warmer than gloves. If your hands get particularly cold, a lightweight glove within a mitten works well. Two tips for those whose hands get particularly cold include 1) putting on hand lotion before you put your gloves or mittens on or 2) using those chemical hand warmers you can pick up at CVS.
Hats: A warm hat with a wind barrier will keep your head toasty, but make sure it covers your ears well! For some folks a good fleecy headband (such as those made by Skida or Craft or Smartwool) will suffice.
Face protection: A Buff around your neck can be pulled up over your lower face if necessary, or, if you get to warm, is easily removed. (It can easily become a headband, too!) A balaclava (face mask) will protect your entire face. As with hand lotion before you put on gloves, some Vaseline or Aquaphor applied on your lower face before you run will provide some additional protection.
Eyes: Sunglasses for during the day, or a pair with clear lenses when it's dark out, will keep protect your eyes from the wind.
And, when you're done running, don't hang around in those running clothes for too long, as you'll get chilled. Bring a change of clothes with you so you stay warm.