Temples and shrines, for example, are open on New Year's Day, because it is a favorite time to go and pray for good luck in the coming year.

I took students from a Pacific Northwest college to Japan one January Term. It was an excellent time to go, because the temperatures were what they were accustomed to (daytime highs of around 5°C--low 40's Fahrenheit) at home, only without the rain. A lightweight wool coat or a trench coast with a zip-out lining is perfect for this kind of weather.

If you plan to visit temples, where you are required to take your shoes off, wear thick socks. Otherwise, walking on cold tatami and wooden floors in thin socks will chill you to the bone. (Voice of experience here. Putting on an extra sweater and drinking as much tea as I could stand did nothing to ease the chills I acquired in a rural temple. Only a steaming hot bath did the trick.)

One of my students wore thick socks with sandals, and he was fine until we went to Hida-Takayama and encountered the slush from a recent snowstorm. Otherwise, we were comfortable and enjoyed the nearly constant visibility of Mount Fuji during the eastern part of our trip.

Given the choice, I'd much rather visit Japan in the winter than in the suffocating heat of August.