It you are spending 10 days in Japan in the winter and like the snow, then spend 2 days on Noto Hanto is a good option. Book a room at a Wakura Onsen Ryokan and enjoy the local kani (crab).
The Kenrokuen in Kanazawa is famous for snow scene.
The easiest way to get there is by the Thunderbird train from JR Osaka Stn or Kyoto Stn. I stayed at the Kagaya Ryokan three years ago and it was very nice service wise and food wise.
Added:
Here is someone else's photos of this hotel. Masako san seems to be the hostess assigned to all English speaking guests.
http://www.flickr.com/photos/lear_sh...7594107031046/