Hi Andy!
This is a pretty hard one! It would really depend on what day trips you would make.
For instance a one way ticket
Tokyo - Kyoto will cost ¥ 14,320
And Osaka - Nozowa ¥ 12,000
This by itself would almost pay for a 7 day JR Pass which is 28,300yen,
However add a day trip to Hiroshima by Shinkansen and you could save a good ¥ 19,900 and you would have covered more than the price of a 14 day JR Pass.
Taking the above into mind, I think that a 7 day JR Pass would be the best option to cover your travel from Tokyo up to Nozawa. This would give you great flexibility to make day trips as you would like (worst case you break even compared to normal tickets, if you don't make any day trips).
This would also work very well with the last part of your itinerary. The best way to travel between Nozawaonsen - Hakuba is best done by bus and a JR Pass would not be that helpful here.
As for Xmas, until the west Christmas is not a national holiday in Japan and people have to work. You may see a little more traffic because of foreigners moving around but there's not need to worry about tickets and such (except if you want to go to a restaurant, because it is common for Japanese to take their loved one for a romantic dinner on Christmas Eve).
I hope this helps!
-Daniel
