The Nutshell tour is really a multimodal combination of train, boat and bus travel coordinated to tour a scenic route. The "tour" should be offers year round as long as the various modes of transportation are operational.
I suspect that in trying to book a 20 December start you are too far in advance of the train schedules. This would be like trying to book air travel for 28 July 2015. Try again in 10 days. (The Nutshell schedule shows the autumn timetable going from 29September to 13December. You will need to wait for the Winter schedule to be published. Keep checking).
The Hardagerrvidda should be snow covered and you will likely see Norwegians enjoying the end of Fall beginning of winter in the mountains. You may have to share train car luggage space with skis.
As to climate, see:
https://community.ricksteves.com/travel-forum/norway/weather
The Flåm route down to the fjord will not be as spectacular as a spring/early summer trip. The water falls will be frozen or at least not cascading with spring summer runoff. But winter is a season of silent beauty.
Norwegians enjoy life. Things could be slow from Christmas eve until after Boxing Day in terms of tourist things. I don't have specific Xmas experience, but found that during Easter wroute down to downslo shut down from Maundy Thursday until after the Monday after Easter holiday. All the Norwegians appeared to be in the mountains.