Yes, and to reach Takayama in the winter, the handiest way is to take the Shinkansen to Nagoya (all Shinkansen out of Tokyo stop at Nagoya, about 1.5 hours) and then take a regular train out of Nagoya to Takayama.

In the summer, it's kind of fun to take the train out of Shinjuku Station to Matsumoto and go over the mountains to Takayama by bus, proceeding on to Nagoya by train, but I wouldn't want to try it in February.

Takayama is a well-preserved old town, and in the winter, they brew sake, so perhaps you could tour a sake brewery and get some free samples.