I know I don't loosen up as well in cold weather. That said, I still commute daily all winter. Granted it's in CA, and I rarely get below freezing. 40s are common. I know this is warm for some of you. Sorry.
I find, depending on the temps, the following things helpful:
Head covering. Earband, or buff, of if it's really cold, watchcap
Hands: Mine get cold easily. Glove liners for a biy cold, full on ski gloves if it's really cold.
toe covers
I always go with a base layer. I like a fleece jersey, or if it isn't cold enough for that, I have one of those super-light jackets that stop the wind.
But in any clothing, the juices don't flow as well as they do on a nice warm day.