Driving to Montana in November/December – weather/road conditions?

I am thinking of hiring a car for a couple of days and driving South from Banff in Alberta, where I am currently living, into Northern Montana, possibly to Glacier National Park. I want to do this fairly soon before the winter really sets in. What are the weather conditions likely to be and is it safe to drive in a normal hire car? I am an experienced driver in normal conditions but not at all in snowy conditions. I would mainly be sticking to highways, maybe visiting St Mary in Montana, no further South.

Thanks

It’s actually kind of funny you mentioned that sort of trip, because I’m looking to do something very similar and looking for the same answer. I want to drive from Washington State over to Glacier Natl Park in Montana and up to the Alberta border to see Waterton Lakes Natl Park. I’m wanting to do this at the end of November. I’m trying to find info on driving conditions also. Anything you find out, please let me know and I’ll try and do the same. Thanks