Japan doesn't celebrate Chinese New Year, outside of emigre communities, so that will be no problem. When the Japanese adopted the Western calendar, they moved their New Year's celebrations to match it, so the major holiday period is around December 31-January 3.

The Japan Rail Pass is definitely worthwhile for an itinerary like that.

However, be prepared for cold and heavy snow in Hokkaido and Nagano. At the same time, Tokyo and Kyoto will be somewhat warmer (daytime highs between 5°-10°C), with snow unlikely. And as people frequently say in this forum, Kyoto and Osaka are very close together, so there is no need to book two hotels. In fact, Osaka is not that much different from Tokyo from the point of view of the first-time visitor, so you might want to use your JR Pass to visit another city.