Don't get caught bare naked in the cold! For winter running in Kansas you need layers of water wicking, water resistant, wind breaking materials. In the cold, blood rushes away from your extremities to protect your vital organs so you must protect your fingers and toes! Keep in mind visibility - choose reflective and brightly colored materials.
Winter running gear by body part:
Head and Face
Trap in heat with a beanie and protect ears from frostbite with ear warmers. A fleece neck warmer is a must. And when the freezing wind is all up in your face, try a balaklava underneath your beanie and neck warmer.
Trunk and arms
Wear multiple breathable layers with the innermost layers water wicking and the outer one wind and water resistant. A vest over the top is a great way to keep core temperature up, plus they look good and usually have handy pockets!
Wear two layers with the outer layer in a wind and water resistant mitten as opposed to gloves. Add hand warmers when it is really cold. As soon as you open the package they start working so don't open them up the night before! I store some in the glove compartment of my car.
Keep leg muscles warm with running tights but unless you are stuck in the 80's keep the running shorts in your drawer. For added protection, wear compression shorts underneath those tights. Fleece lined tights are too hot for me no matter the temperature but many runners swear by them.
Wear slightly thicker run socks than you usually wear. Avoid socks that are bulky and don't double up as you will find your shoes are suddenly too tight and that is a no-no. In the event of snow, try yak tracks over your shoes.
If the windchill is below zero or ice is on the ground, running gear won't be enough. Skip the out of doors and cross train or run indoors.
RRKC is not affiliated with a brand, but Coach Amy has had personal success with Nike tights, Saucony gloves, Brooks and Adidas jackets/vests and Under Armour's water wicking primary layers and face/neck/head gear.
Happy Winter Running!