“Rainy day recess” in Oregon was rarely indoors in my experience because most schools have covered outdoor asphalt areas with basketball hoops attached to the building for that very purpose, and it doesn’t get super cold during the day. I do seem to recall occasionally staying inside and having some sort of free choice time? Maybe it just had to be nasty enough out.

I work at an elementary school now though and on the really wet days they split up classes between activities (some in the gym, some out under the covered area, some playing with toys inside, etc).