It is a nice idea a heated tool closet. Except as mentioned before don't pull a nice warm tool out into a freezing room it will get covered in condensate and need to be acclimated to the shop temp. I think it would be better to leave the tools in the main shop and let then heat up with the rest of the shop.
I am originally from Michigan's UP and used to dealing with the extreme cold as well.
I plan on putting in overhead radiant heater when I move out of the basement.