Well if you have your mind set on Whitefish-you're making no mistake buddy. It's amazing boarding there with literally no lines. (save Family Day week in Feb. and New Years)
Now to roads-it depends where you are planning on crossing the boarder- Coutts is probably the largest and most congested boarder crossing through Alberta-Montana (took us 2 hours of waiting in a kilometer long line
) so i suggest veering away from there, especially on holidays or Fridays (think Del Bonita crossing) .
Yes, specific parts of Big Mountain can be closed from time to time. They have a special chair (chair #4?)that is used only to relieve congestion of the main chairs when lines get busy. However, even on a holiday you are only looking at a 3 minute wait in line. At anytime you can expect maybe 5 runs of the hills 90 some runs to be closed off-mainly around chair 4 and the backside Hell-roaring.
As for the snow, anytime within January-March is perfect. If you stay a couple days expect a couple inches every night-however two years ago when I visited we received close to 2 feet in 4 days
Wolfram-Alpha says the distance is 194 miles only but it seems a lot longer than that. After you reach the boarder crossing it is a 3 hour drive.
Hope you play with all of the big's 4000 acres-it truly is a fun mountain, especially when the fog is so thick you cant see 15 feet in front of you and the snow is piling down.