So all North American Bears stay in hibernation from fall to spring. Do any not hibernate? Do any come in and out of their dens during hibernation?

Of the three species of bears in North America, grizzly and black bears hilbernate during the winter. Among polar bears however, only pregnant females hibernate, while males, females with large cubs, and females with no cubs at all stay active out on the ice.
In addition, while nearly all black bears hibernate, some that live in places like Mexico or Florida where it's always warm and there's some food around have very short hibernation periods or don't hibernate at all.
As for bears coming out of their dens during hibernation, sometimes they'll come out if a dog, a snowmobile, or something else startles them awake. They'll occasionally also leave their den and wander a bit if it's an especially nice day. This is rare though.
Hope that helps!