I am currently running my rigs in an unheated space. I'm hoping that even if outside temps get down to below freezing there won't be any issues with the rigs seeing as how they put out enough heat to keep the surrounding area well above freezing. I may build an enclosure if necessary.
So what's the lowest ambient temps you've run rigs?
LOL! Well, during the summer I definitely fun the fan over my gpu rig and now that it has cooled off I don't need it so I can turn that off to save some $$$fan money.
But I do run mine in a basement which has really cold temps in the winter so yeah, "unheated space" just like you. Frankly, I haven't seen any issues. The temps are still in the 60's sometimes high 50's.
I think you'll be fine as long as you are in a "space". Just remember that when it gets hot again you might actually need some airflow. I know I did!