According to the calendar, end of January is the most cold time of the year.
However, it is rare to have heavy snow in Tokyo...
It has started snowing before noon and we had about 5-10cm (2-4inches) deep snow in central Tokyo. Under these circumstances, public transportation such as Train, Subway, Metro, Bus are delayed or you have to take another available option, or you would be stuck in the worst case scenario.
Forecasted highest temperature of the day was 4℃ (39℉), but it felt like 0℃ (32℉) or less!
Freezing, but quite experience!
Have fun in Tokyo!