I would find out the recess policies in writing first...ask for a copy, I would assume most districts or schools have one (ours did). Any form of rain they stayed in. Then there were temp regulations, wind chill, etc.
I always sent my child over prepared. She had to walk to the bus, and stand out there in sometimes severe rain (altho one nice neighbor mom right at the stop would let kids stand in her garage in downpours with our permission..even when her kids were off to Middle school), so mine always had rainboots, thermal rain coat (and a thinner one for warm days)...boots, coats, snowpants, hats gloves, etc...all decked out for the days anticipated weather. Nothing like NOT being prepared.
Sadly, she was one of few dressed that prepared if memory serves....