Here "Ryokan Ontake" seems to refer to the inn [ryokan] of the following link.
- Ryokan Ontake in Nigorigo-onsen
https://www.ryokan-ontake.jp/eng/This ryokan is in Nigorigo hot spring resort in Gero City in Gifu Prefecture, near Mount Ontake, which stands across the boundary between Gifu and Nagano Prefectures.
It sounds not easy to reach this inn during the snowy season in winter.
No railway station is nearby; plies of snow and icy roads may well be hindrance to your access.
One pick-up bus is scheduled per day to run from Takayama Station, departing in the afternoon.
The one-way fare is 1000 yen.
https://www.ryokan-ontake.jp/eng/access/I think you had better avoid driving a car to this inn in winter.
According to the latest news in Japanese on the website,
there are plies of snow and icy roads within a radius of 15 kilometers around the inn,
you should fit studless tires or tire chains to get there by car,
you are expected to arrive by 6 p.m.,
and it is very dangerous to drive a car at night around the inn.
Do you think this is doable in a day given that this is winter? It sounds a little ambitious; your timeline is to be shown in my next response.
Due to the low frequency of Shinkansen trains making a stop at Kurobe-Unazukionsen Station,
you reach Toyama Station too early to get prepared for your bus ride to Shirakawa-go.
The arrival of your express bus at Takayama may be delayed and the departure of your pick-up bus may be advanced; so, when you plan to reach this inn on the same day, you cannot have much time for sightseeing in Shirakawa-go.
I suppose it should be better to stay overnight around Takayama Station then head to this ryokan on the following day by bus in the afternoon.
- Japan Guide: Highway express bus timetables
https://www.japan-guide.com/bus/shirakawago.html