Cotton kills. No blue jeans. No cotton long underwear. No cotton socks. Instead go for polypropylene, fleece, wool, nylon, and other artificial fibers. See note on goose down below.
Layers. Adjust layers to your level of activity in order to stay dry and warm. Loose-fitting.
Outer Layer: Windproof, water resistant. Large enough to fit over all the other layers!
Insulation Layers: fleece, PrimaLoft (or similar) artificial insulation, wool, or goosedown. Note: Typically goosedown layer is only used when you are stopped -- must be kept dry.
Wicking Layer: polypro (or similar) long underwear.
Extremities: Head, hands, feet. If you are cold, put on a hat! Windproof, waterproof, adjustable (layered). Bring spares, especially socks. Possible vapor barrier liner inside socks to keep your boots dry. Hat can cover ears. Tight = cold, loose = warm.
Helmet: Need a close-fitting hat that fits inside your helmet.
Face: Balaclava and/or face mask.
Sun: Sunscreen, sunglasses, goggles. Note: metal-framed glasses can be a problem.
When you get going, take off insulating layers. You need something to put these layers in -- i.e. a backpack, somewhat larger than you would use in other seasons.
Water bottle -- large mouth, very good closure, and resistant to cracking in cold. Possible insulating layer.