Are you sure they weren’t saying “bon hiver” (French for good winter)?
You know, this caused me to do a bit of research. Northern Exposure had almost a cult following, and still to this day, there are blogs and websites, and there is endless discourse regarding every little detail of the show, and you are right, they were all wishing each other "Bon Hiver".
But it really sounds like Boney Bear, and it's funny how I made this work in my mind all these years. Alaska, bears, winter, hibernation, and how thin and 'boney' a bear can be in the spring.
And actually, now that I think about it, the more boney the bear is in the spring, probably, the more lengthy and intense winter was, so to wish someone 'boney bear' is actually wishing them a long and very intense winter..
So good catch, I stand corrected.. OP, if you are still listening, I wish you Bon Hiver, and the images posted above are both awesome. You live in what I consider to be a beautiful spot.