Well this might be a shock to you..
They go outside almost always. It has to be raining, or close to below zero before they will keep them in. They have to wear snowpants, boots, gloves, coat, hat everyday to school it does become annoying but they need it.
If they stay in which is rare. In kindergarten they would have "choice time" play with whatever they want in the classroom.
In older grades I believe they use the gym to move around or do something fun in the classroom.
At our school we don't have recess monitors, the teacher's monitor recess so they are always supervised whether they're outside or inside.
The only break I know of for our first grade teacher is lunch, and when my daughter has art,gym, music those type of classes.
Also be prepared it takes ALOT to get the school's to cancel for snowdays. Last year my daughter's school was being stubborn and wouldn't close so by 2pm that day they let out early and I had to walk up with a sled to get her home, my car couldn't make it the snow was to deep. The school buses were fine but we're considered "walker's" so I it was walk or drive my car.