So I am wondering if I should buy a Hakone Free Pass even though I will only need an one-way train ride from Shinjuku to Odawara.No. If you want to use the Hakone Free Pass at all, you should buy it at Odawara and pay for the Shinjuku-Odawara section separately.
Besides, we may not want to do the cablecar, ropeway and boat this time.
Whether the pass pays off or not depends on your definition of "and possibly explore 1 or 2 towns". Odawara - Miyanoshita - Odawara alone will not justify the purchase of a pass.
From Kanazawa to Matsumoto, we are planning to rent a car and explore Ogimachi on our way to Takayama.
Ogimachi can be easily accessed by public transportation. No car is needed for that part of the trip.
Besides, there is a ryokan located between Takayama and Matsumoto that we want to stay this time.
Public transportation does not provide easy access to that ryokan?
After checking the train schedules, driving seems to be the most effective way for that part of our trip.
Trains don't get you far in that region of Japan. Kanazawa, Ogimachi, Takayama and Matsumoto are connected by bus.
Any comments/suggestions on our tentative itinerary will be appreciated, e.g., driving conditions in Dec. in the Ogimachi-Matsumoto area, is it too hectic for all the one-night stays, etc.?
There is a risk of snow covered roads. If you are not familiar with driving in winter conditions, I would think twice about renting a car in a foreign country. If you are familiar to driving in the snow, I see no problems.
As for the pace of the trip, yes, I think just one night each for Kanazawa, Takayama and Matsumoto is rather fast paced. I think an additional stop or two-night stay would make it more pleasant.