Really, the front of my body is generally warm enough, as a cow gives off a lot of heat.
Last year, she freshened at the end of November, so the curd set was wonderful. She's been in milk for just over a year now and I'm still getting great cheese, just not as much of it, as she's down to a gallon a day.
However, that being said, my cow doesn't have access to pasture. She does get lawn trimmings and I cut longer grass from the fencerows, etc., during the summertime, but her main feed is hay, mostly alfalfa/grass mix. So, my experience is probably different from most.
Back to one of your initial questions: If your creamline milk comes from a local dairy, you may want to call them and see if they slow down or stop production during the winter months. There is a local organic dairy in my area that dries off all of their cows during the winter so they can go south and leave the farm to hired workers. However, the big organic dairy that produces much of the creamline milk in my area has a huge herd and the cows are in freshening rotation to keep production consistent throughout the year.