As long as there is no snow on the ground, I'll play all winter in the Philly area. Under Armour is a miracle fabric that keeps me pretty warm, usually a mock turtleneck under a cotton or wool sweater vest. I'll wear a fleece over that, but I usually end up taking that off during the round unless the wind is blowing, but I might not play anyway if the wind is blowing. I'll wear my Philadelphia Eagles ski cap, winter golf gloves and wide wale corduroy slacks and I'm ready to go. And, of course, I walk. Riding in a cart is crazy in cold weather. You will never warm up.
I take you haven't seen guys in carts with covers and propane heaters. I've played with them at times when they are too warm and I have to walk a bit to cool off.