This might be my 1 second theory, but Reimu might indeed "breathe through armpits" in a way.
For all the time we see her, the general composition of her clothes is unchanging (bare shoulders, detached sleeves in particular). So her body likely "grown" into that uniform and adapted to extencively use shoulder region for body heat regulation and skin's "sweat waste disposal" feature. Torso also benefits from vest as it, basically, constanlty vented through rather big holes in all directions.
It is not safe to operate your Shrine Maiden™ with it's radiators obscured. Doing so anyway constitutes a fire hazard and voids your insurance in the event of damage.
Updated
There's not enough space!
WH... WHAT DID YOU SAY...!!?
Why are you
blocking them!?
Yeah, guess this is what you get with clothes you're not used to.
AH!
So the reason you keep your arms uncovered all winter is because you breathe through your armpits!