I have always enjoyed camping and do a lot of it with my kids who are involved in scouting. We have our upcoming "polar camp" in February in which we spend a weekend outdoors no matter how cold it is. We do have a large outfitter tent with a woodstove so it does stay above freezing for sleeping, but you can really manage well outside even in below zero temps if you prepare and dress properly. Eating enough throughout the day and drinking water is very important too - you will perspire even when it's cold out with heavy clothes on. A dry set of clothes to put on right before bed is a very good idea too.
Our "record" cold temp for polar camp was -18F - which the scouts are always proud to announce ;- ) We do most of our camping in more reasonable temps though of course.