To throw a spanner in the works ... if you get a snow storm in Tokyo you are in trouble too.

I got stuck in CTS in Jan this year for about 8 hours - snow everywhere all the time in Sapporo but Tokyo isn't used to it and the airports were closed. Everything was cancelled for hours and CTS was chaos with how to get rid of all the people. Narita flights were running again before Haneda .. but everyone was on standby and almost all foreigners missed their connections.

Anomalies of snow, etc aside I think you will be fine but have never done it myself