Ours are shut after school hours, you cannot stay and play, and they don't re-open either. I suspect behavior just like the OP was taking place, and rough housing, and they were probably worried about property damage, clean up, and liability. So now no one can use it.
Public schools in NY can not turn the public away unless they 1) have a dog 2) are using language that is abusive 3) bullying children 4) are a registered sex offender. If anyone is there that the school doesn't think is ok (as in, an adult w/out kids or any one of the 4 options above), then they have to call the police. That said, they have doors locked policy (all the time) for the safety of the children, so only the front door is open. If you want to pee, you go arouuuuund the school, pee, and then you can exit any door you want. You are also supposed to sign in and out, which is a safety thing as well. Since all the schools around here provide after care for the children of working parents, no one would get to use the playgrounds during the week at all - after care goes until 6:30pm. Even in summer, kids eat dinner etc., so that would suck big time! This way, kids with parents can join in with the kids who are part of aftercare, but older kids (like ones who ride bikes etc.) are supposed to go home and come back w/a parent. But they don't always. They are still responsible for their behavior and the monitors can and do kick kids off who don't behave.
The private schools do NOT have to allow any kid on the playground that is not with their class. Traditionally, families who belong to the school do use the playgrounds whenever they want - I bring ds (3) to pick up dd (10) and we go 30 min. early so he can play on the playground at her Montessori school. He's pretty good about saying when he needs to pee, but he's also been known to 1) poop in the backyard 2) pee anywhere, even right on the street while we are walking the dog!, 3) think peeing in public/outisde is funny. We've had a bunch of discussions about where it is appropriate to pee if you are outside, like if we are on a trail etc. and WHEN it is appropriate to pee outside, and when it is not. Since he gets it (hasn't done anything naughty pee-wise in oh, probably 3+ months now), and he's about the same age as your ds, I'm guessing your ds is also developmentally ready to learn that peeing on school playgrounds is NOT ok. Ever. If he doesn't get it, then I would not let him play there, unfortunately. He'll get it, I only hope he gets it before he isn't allowed to play on the playground.
Hugs for the crappy treatment, mama.