I want to see the snow and mountains!

Hi!

I’m travelling to Japan from 30 Dec- 10 Jan.
I’m spending a few days in Tokyo and then Kyoto but the main highlight for me is to see some snow and stay near mountains in a ryoken with an onsen

I had been looking to stay in Yamagata area and doing trips to Zao Onsen and Ginzan Onsen, I am not driving and will be using bus/trains for this. I’m planning to stay for 3 nights.

Does this sound like a good plan or does anyone have any good recs for destination to stay which fit my wintery mountainous escape dream which is reachable from Tokyo? Thanks!!!