Tokyo winters are not as cold per se as North America but Tokyo is a very draw winter every year. I've had Canadian friends who say it feels colder in Tokyo! The coldness likes to bury itself in your bones, that is how the cold is here.
But as of the last week it's been oddly warm, more like spring weather, that of April during the day time. As for snow we haven't had any that stuck, just some wet flurries as pictured in this photo. And this was about 30 minutes at 3am in west tokyo.