Japan in January.

[Ohwhatfuckeryitistoride]

I know its going to be cold(ive looked it up and it says cold but dry and bright) but how doable would be 10 days, tokyo, osaka and kyoto? Its a organised trip, and the price is very affordable. Am I mad?

Generally warmer than the UK, but definitely not warm. You'll be fine though, I would definitely go, layers that you can add or remove throughout the day are your friend.

Likely to be cold and bright - low humidity and (often) clear blue skies. Rarely below freezing in the cities. Will feel warmer than similar temperatures in the UK due to the lower humidity.
You are likely to want layers as previous respondent said. It may rain - but cheap brollies are available in every combini (convenience store).
NB lived in Tokyo for about 10 years.

Should have said - definitely doable, and one of my favourite seasons when I lived there.

I was in Japan in January. Tokyo was lovely, blue sky and sunshine. Cold but nice and fresh and fine with a proper coat. I was also over on the west side of Japan which was very snowy, also cold but had a great time. Tokyo was very quiet which was great.