Heated water is nice for people, but it is not necessary for chickens. If you don't have heated water, you do need to carry down fresh water each day.
I am afraid to ask how many chickens do you have in that set up, cause it is very small. A lot of chickens in a small area can really build up moisture FAST, from their droppings and their breath. Damp chickens are cold chickens.
So contrary to what you might think in order to keep chickens warm, you need to add more fresh air, better ventilation not more heat, not trap the heat mentality.
I do agree with the plastic wrap around the run, but you need it several inches short of the roof. Almost ALL PRE FAB coops do not have near enough ventilation. If you see moisture on the inside, you do not have enough ventilations.
Deep bedding, as in REALLY deep will help. In a very small coop, one really needs a poop board, or hammock to be able to remove the poop daily. Otherwise ammonia and moisture will very quickly build up.
Mrs K