I'm not familiar with winter boots per se, but what brands are you referring to? Some consider Clark Desert Boots as winter boots, some think Dr Martens and Timberlands are winter boots, some only consider Ugg to be proper winter boots. If you're looking specifically for these, then lots of thrift/2nd hand shops around Tokyo carry them.

You will find plenty of boots in second hand shops or thrift stores. Just inspect them carefully before buying them and they'll last the duration of your 2 week trip.

I'm not sure if there are rentals of these winter boots. I assume you are not referring to ski or snow boots yeah.