Hitch hiking is common in the mountains and you could do that. However people have been murdered. I know of three cases where people were murdered in Colorado because they were hitch hiking. A couple of years ago they found a body near Aspen and it was said he was likely hitch hiking and murdered. A few years ago around Fairplay a women was murdered, she was hitch hiking from national forest. About 9 years ago a snowboarder was murdered hitching.
There are cabins in the woods, but it takes local knowledge and hiking to get to them. You would need to know where they are. You would need snow shoes. I know of a few, but I don't know how often people stay in them or if there are rules. Camping in the winter is possible. People do this, google winter camping. It would require some equipment. I know people when I worked at A-basin who would build snow caves and sleep in them. Fucking crazy! People do live in the woods in the winter, nuts! It does get polar bear toe nails cold, like double digit below zero. Sleeping in a car in this kind of weather is brutal. One of those camper rapist vans would be better. There is a lot of National Forest in summit where you can legally camp in one place for up to 7 days.
I saw this cabin in the summer. You would need snow shoes to get to it and it's a hike. I don't know who stays in it and how often or if there is a waiting list. I don't think it's an official BC hut.