Its possible but you may have a big heating bill. I grow peppers and tomatoes in my greenhouse all winter but I also keep my greenhouse above 60 at night because I mostly grow orchids and tropicals.
I use a small milkbarn utility heater most of the time but I also have a propane Buddy Burner I can turn on for the really cold nights.
I have a remote thermometer so I can monitor the temperatures from the comfort of my living room.
