Just wanted to add (to ksandness' post), that even if it does snow when you are there, this hardly presents a problem within Tokyo.

You'll find that at least 95% of women in the city make no concessions whatsoever when it comes to footwear and will be wearing the most inappropriate shoes for the slush (which is what Tokyo snow rapidly becomes and then remains for most of its short life).

Here's a thread about the freak snowfall that closed Narita in January last year.

Bear in mind that one of the most popular times of the year to visit Japan is October, and that's when typhoons could wreak their havok.

All in all, I consider February a good time of the year to visit Japan - certainly preferable to June, July or August. Even in October this year I was getting devoured by mosquitoes in gardens within the centre of Tokyo, so, in my view, February would be a better time than September or October to visit
some of Tokyo's glorious parks.

The downside of a February visit for me would be the constant static electric shocks from the dry air. My husband has particularly dry skin and we can't even graze against each other without sparks flying. Thankfully, electric earthing devices can be found from stores such as Tokyu Hands. Even this does not discourage me from winter visits to Japan.

On the plus side, the air is clearer so the views from high buildings should be particularly striking and you're in the running for a Tokyo view of Mount Fuji (which didn't appear once between 2nd and 14th October this year).