Only problem would be drying time and freezing.
I am in Albuquerque, I just did a un heated space yesterday and finished at about 3:00 in the afternoon, with first coat of tape & mud.
Scope of the work is a un attached garage that was converted to a apartment years ago.
We opened up a wall and added 2 sets of 6' french doors and replaced 3 windows, We had to open the ceiling so electrician could jump the wires out of the wall and into ceiling.
So really not a lot of mud work.
I used straight 45 min hot mud and this morning was still not dry, firm enough to scrape, but not completely dry.
I got a space heater going and warmed the place up. By lunch time had a second coat of hot mud and a complete skim coat of topping on it.
Just a little sanding in the morning and will be ready for paint.
Just get a little heat in the enclosed room and it will be fine. Not ideal conditions for drywall, but is doable.
I have done this same thing many times over the years, never caused a issue that needed to be fixed later.