Overnighting in Hakone on the 25th and 26th in Dec, would be staying a night either in Hakone Yumoto or Miyanoshita and another night near Lake Ashi in either Moto-Hakone or Hakonemachi.

A couple of questions which I'd need help with:
1. Any chance of a light dusting of snow or frost around Lake Ashi during that period?

2. Where are the view points around Lake Ashi for views of Mount Fuji? Or more specifically, photography hotspots.

3. In view of Question 2, would Moto-Hakone or Hakonemachi be more suitable places to base myself at?

4. I'm looking into several places around Lake Ashi for overnighting.
In Moto-Hakone:
Hana no Yado Fukuya
Lakeside Inn Charlotte
Musashiya

In Hakonemachi:
Hakone Hotel
The Hakone Takuminoyado Yoshimatsu
Yuugiriso

I know the Hakone Hotel has wonderful views of Lake Ashi and Mt Fuji. However, I'm not too keen about the dining options. I am not going to Japan for French food!

At the moment, I'm swaying towards Musashiya. Seems like a value-for-money place to me. Hana no Yado Fukuya and Hakone Takuminoyado Yoshimatsu appear to be more costly but I think that could be due to the kaiseki dishes, so I can't complain.

Would anyone have any other suggestions and recommendations based on your experiences?

Thanks in advance for your help.