Usually 60 – 70 degrees of 50% humidity will allow sheetrock mud to dry overnight. How I wish I could find the opportunity to work in such weather. What you will find is the colder and / or wetter the atmosphere, the longer the dry time for sheetrock mud. Please do not allow the mud to freeze. As Karl has pointed out in his articles, you will know by the foul smell if it has. A heater of appropriate design and size will assist in cold weather.
Ideal Temp for Drywall Mud