I've taken the Canadian twice, both times in early February. They usually start posting the super-discount fares in mid to late December, roughly half off the standard price (including half off the "discount" price). We looked into it last year and the prices for a standard double room were roughly $1k per person. The train is quite empty and you get very nice personal service from the various attendants, including the on-board steward who shares stories and wine/beer/bubbly tastings every evening before dinner. There are no restrictions on the parlor car except that if they have any Prestige customers, the first row of the dome is reserved for them. As it happens, both times we didn't have any Prestige, so there were no restrictions at all. The entire sleeper section fit into a single seating in the diner, which was very pleasant.
The good news about early February is that the days are getting slightly longer after December 21, and remember that the earliest sunset is actually around Dec 15. We had no problems with scenery. Also, that far up north storm systems tend to be small and move through quickly, so you could have heavy snow for 4 hours and clear 4 hours later.
My experience is a bit out of date, so if you are thinking of a late January or February trip check back with us in December for the latest info.
I took the Canadian with my mother and with my then 10 year old son, and both times we had a fantastic time. Highly recommended!