I've never done a week in the snow on a bike as I prefer my winter expeditions by the pleasure of skiing instead of biking.
However, I have done overnighters up to 4-5 day trips in the height of winter.
Here's a Youtube short from a January trip i did a few years ago.
It is fun, it is cold. Keep in mind a person needs to eat a LOT of calories (a half a stick of butter per person per day is a good supplemental ration) and melt a LOT of water when you're in the hinterlands in the winter is my primary advice. No alcohol stoves in the winter if you need to melt snow for drinking.
Lots of tent time is de riguer as well for most of the US.