Will any of these road closed in Feb/Winter?

Hello,
I will be travelling by car from Tokyo to Yokohama-Kamakura-Hakone-Owakudani-Mt.Fuji ( Will stay near in Ubaya Ryokan and will only upto here no hiking up hill)-Karuizawa-Shibu Onsen ( Monkey Mountain Oark)-Matsomoto Castle-Ikaho-Nikko-Tokyo in early February 2020.
I had been driving these roads few times but never in winter. Can any one tell me if any of the road will be closing in the first week of February due to snow esp the narrow road from Shibu Onsen to Monkey park, Hakone to Owakudani and the winding road uphill and downhill to Nikko? Will iy be save to drive in winter only with snow tires?

Thank you in advance for any feedback and advice.

Between Ikaho and Nikko, Route 120 through the mountains via Numata will be closed, but the Route 122 through the Watarase Valley will be open. All other roads in your itinerary will also be open.

Also between Karuizawa and Shibu Onsen, Route 292 through the high mountains is closed, but the faster route via the expressway will be open.

Uji san! Thank you very much! You have been always very helpful all these years!
By the way do you know whether the road from Shibu onsen to the snow monkey mountain park will be closed on fen7/2/2020? I drove once in April and remember the road is very narrow and precarious. Will there be heavily snow covered on this section of road leading to the park?

Uji san!
Further to my message earlier I check the link on snow monkey park:http://www.snowmonkeyresorts.com/smr/snowmonkeypark/information-about-...
It seems the road leading to the car park at ticket booth of 2 km will be heavily snow covered and I need to hike to walk in. I remember the trail from ticket booth to the thermal pool where monkeys bath and return trail will be another 2-3 km totally 6-7 km. is it right? If I drive to the entrance of the narrow path and hike in to ticket booth..do you know whether there is any parking outside of the entrance road? Appreciated

Uji san! Another question:
1)From Karuizawa Hoshinoya ryokan I will drive to Matsumoto to see the castle then to Shibu Onsen. I presume i need to also use expressway?
2) From Shibu I will by pass to Kusatsu before going to Ikaho. I presume all the way there is expressway too?
3) Nikko will Chuzenji lake be frozen? Road from center to the lake ok? What about onward to Fujiware fall?
Appreciated!

By the way do you know whether the road from Shibu onsen to the snow monkey mountain park will be closed on fen7/2/2020?

Yes, the small road to the parking lot near the park is closed during winter, but the road to Kanbayashi Onsen is open. Access to the monkey park is explained here:
https://www.japan-guide.com/e/e6028.html

It seems the road leading to the car park at ticket booth of 2 km will be heavily snow covered and I need to hike to walk in. I remember the trail from ticket booth to the thermal pool where monkeys bath and return trail will be another 2-3 km totally 6-7 km. is it right? If I drive to the entrance of the narrow path and hike in to ticket booth..do you know whether there is any parking outside of the entrance road?

The walk from Kanbayashi Onsen to the park takes about 30-45 minutes.

1)From Karuizawa Hoshinoya ryokan I will drive to Matsumoto to see the castle then to Shibu Onsen. I presume i need to also use expressway?

No, you don't need to. You can also toll-free roads, but you could be spending considerably more time.

2) From Shibu I will by pass to Kusatsu before going to Ikaho. I presume all the way there is expressway too?

The direct road through the high mountains is closed, so you will have to make a detour. I think the fastest alternative is via Sugadaira Kogen.

3) Nikko will Chuzenji lake be frozen?

No.

Road from center to the lake ok?

Yes, the road between Nikko town center, Chuzenjiko and Yumoto Onsen is open.

What about onward to Fujiware fall?

Do you mean Fukiware? No, the road onward from Yumoto Onsen to Fukiware Falls (National Route 120) is closed as mentioned earlier. If you want to go to the falls, you have to approach from the Gunma side (Numata).

Uji-san

Thank you very much for your valuable feedback. In Shibu I will stay in Rekishi-no-Yado Kanaguya. It shows 15 min drive only to the outside of the path that leads to the monkey park. I intend to drive there and park the car outside then hike in to the ticket booth. The monkey park info stated 2.5 km only from outside to the booth. Is it really 45min to hike to the ticket booth? I will not be staying in the onsen you mentioned.
As we are bringing a one year old infant wondering if 45 min hike just to the ticket booth it may be a problem,
Thank you once sgain

Uji san
Sorry I wrote earlier without looking st the link you provided. By looking at your link, the only way for me is to drive from my ryokan Rekishi no Yado to Kanbayashi and park at the public parking to start the hike as from my ryokan via Shibu Onsen is closed. Did I get you tight?
My apology

Yes, that's right.