For weather checks I use this resource at Yahoo. If you are traveling to Tokyo at this time of the year, I would advise on a warm coat, gloves and hat as the wind can be biting cold at times. If you are going to use the trains then you may boil to death as its usually really warm down there - unless you bring something like a Uniqlo down jacket which are warm but light.
The JR trains and many restaurants go overkill on the heating making it extra uncomfortable when you are on the move - a light but warn jacket will save your bacon.
Lots of folks are sick at this time of the year which is why you will see many folks wearing surgical masks like this - this is because either some folks are sick (and don't want to spread germs) or because one does not want to catch any germs.
It has been raining on and off before the snow so bring a brolly if you have one but if you cant be bothered then you can always pic up a plastic umbrella for about 500 yen from a convenience store if you get caught out in the rain or snow.