Lake Louise, Sunshine, Fernie, etc. are all filled with TONS of available off-piste riding. So I'm not going to tell you about some of my favorite spots! lol
I will say that all of them have spots that can hold fresh powder for days after a storm, even during busy times. Just watch where the other people go and don't go that way. Usually spines seem to have more snow on top (maybe people are scared to get out to them?) and other areas that you have to traverse to. If you stick to the fall line things will be more heavily travelled.
The other thing is I LOVE finding my own secret stashes in places. It's an adventure just to find them! At Louise your best bet would be the top of the world chair or the platter, some of the back stuff is decent too but I find it actually more abused back there.
For riding advice, I'd say xmas day, boxing day, and possibly new years eve will be worth it. Otherwise it'll be a gong show. I was at Lake Louise last year on boxing day and it was great. We stayed in town that night and had to go to the base of the hill on the morning of the 27th (lost car keys) and the line just to get a ticket looked like it was hours long. Then the lift lines were retarded. I would avoid the big 3 like the plague from the 27th to the 30th.