H.W.
I've never known any legal precedent which states "come rain or shine, children must go out for recess in all weather".
What I can tell you is that some schools don't go out on cold/rainy days because the student population is not all able to afford coats and appropriate clothing for cold weather. Not because the parents don't bother, they just cannot afford it.
I agree; I'm not a huge fan of indoor recess myself. Or I wish it could be rotated so that some of the kids could use the gym for it. However, I wonder what the other side of the story is regarding the ten minutes of free time. Was the class acting up so that it took the teacher longer to provide instruction? Was there a 'special' that day (assembly, etc) which took over the recess time? Testing? I'd ask the teacher directly with an open-ended question. My guess, though, is that some of these decisions are made by the principal and handed down from there.
And if they are rotating as to sharing the playground, I would wonder what the problem was which led the staff to make this decision. It's almost always easier to have the kids outdoors than indoors. Is there only one covered area for the kids to play under? Just some questions which come to mind.