Yep, dry and clear. Chance of rain or snow possible.
Main "weather hazard" revolves around the lack of humidity and doesn't affect everybody to the same degree and it's to do with your tendency to get static electric shocks in very dry, urban areas.
If you are a candidate then think about the clothes you will be wearing and try and layer with natural fibers rather than artificial cloth fleeces and base layers. If the build up of static charge continues to be a problem there are inexpensive gadgets you can buy that will allow you to 'discharge' safely before you touch anything. Tokyu Hands has always had a stash of them.
The only issue with snow (which quickly forms a wet grey slush in Central Tokyo) is wearing suitable non slip, water resistant shoes that you can get in and out of easily. You will still be expected to remove your shoes at many destinations.
At the very end of your stay you will find many businesses and attractions will close for the holidays. If there is a crucial purchase you are aiming to get hold of, buy it sooner rather than later. From January 1st onwards (depends on when the particular shop opens) the "Lucky Bag" phenomenon comes into play. You may possibly see Lucky Bags on the 31st December. Most will be a tease, just for show, but you can enquire as some shops might be willing to part with theirs before the 1st, usually not though. "Lucky Bags" are a peculiar kind of sale where 10,000yen worth of goods might be placed in a bag sold for 2,000yen. With some very large stores, such as Muji, there might be a sample bag showing the contents, but generally, you won't know until after you buy the goods. Places like BIC Camera and Yodabashi Camera might theme their boxes so that you at least know if you are getting a camera or audio equipment etc... Depending on the store, they can be a great way of getting inexpensive souvenirs and gifts for those back home. Or not... It depends if you are lucky.