Japan Suggestions: between Tokyo and Hakuba

Hello! I am travelling to Japan for the first time in December/January with my partner. We will be spending the first period of time in Tokyo before heading to Hakuba to ski.

Between Tokyo and skiing, I would like to spend some time in the country side. We will hire a car and I have considered 2 nights in Kawaguchiko to see Mt Fuji and 2 nights in Matsumoto.

Is it worth spending this time in Kawaguchiko? Orrr is it sufficient to do Mt Fuji in a day trip from Tokyo at this time of year?

Any suggestions that make sense between Tokyo and Hakuba would be appreciated.