This reminds me of an annoyance of mine own, the strange dates that people variously assign to the beginnings of seasons. By my understanding the middle of something divides the front half (the bit that talks) from the back half (the bit that kicks) in a fairly even way. So as midwinter - which is an astronomical feast of quite definite timing - occurs in about the middle of December (both pre and post Gregorian reform), the winter that it's said to be the middle of should be the months of November, December, and January. The Celtic method of having Beltane, Samhain, Lunasa, and whatever the other one is, as the doorway dates, makes perfect sense to me.