Where to cross country ski and hike 3/23-4/6?

We arrive and leave from Tokyo and plan to go to Nozawa Onsen for cross country skiing for 3-4 days. Then onto Matsumoto for medium day hikes nothing technical.
Is that a good idea? Or will there be too much snow in late March?

We are also considering:
Kanazawa for the gardens,
Shirakawa-go
Kiso Valley and part of the Nakasendo/Kisoji trail
Mt Kami-Kochi
and hikes around Mt Fuji.

Or should we go to Kyoto and do hikes around there?
Any recommendations will be helpful.

Thanks!