No problem if you put in some effort, very closely monitor things and fix/improve any cold spots you find. There is no reason at all you cannot live out of your camper in single digits nights. Just about every camper has cold weather 'flaws' in one way or another....from ducts that are pinched, to lines along outside walls in the basement, to inadequate ventilation/heat through the basement etc. etc. All of them can be dealt with, but do not expect to just park it there unattended for many days in a row without oversight, at least in the beginning of the adventure. But if you live in it and pay close attention and put some work into insulation, re-routing ducts if necessary, ventilation (really, air flow throough) the basement etc. Tons of good threads on insulation and cold weather improvements (look in the TCUniversity to start with.) That Lance is a good base to start from, but I bet you find some big improvments you can make.
Though it isn't practical to winterize constantly, you do need to be prepared to do it in an emergency (no propane, no battery power, blown converter, dead furnace etc.). Do you have an air compressor in the shed? It is good to have practiced winterizing a number of times (whether using air or Pink stuff) so that the first time you do it isn't in a blizzard and seriously cold. That way if you run out of propane (I'd get a 100# bottle rigged up to connect to your system.....you'll go through propane pretty fast) you'll have the dril down. Practice practice practice.
Go for it!
PS: We are living in our camper right now, full time, in Colorado and winter is here. We are sort of splitting time between our house in the mountains (which is now much more inaccesible due to the floods and washed out roads.) It is really nice being able to live warm and comfortably in the camper in the middle of winter weather in Colorado; I'm sure you will do just fine in your scenario.....