Of course. "injuries" don't matter, only serious and fatal ones do. A scratch is nothing and is healed in a couple of days. Even breaking a leg should not be considered serious. It's annoying, esp. for the parents, but it's in no way life-threatening.
Although I'm sure it has happened, it seems unlikely that any kind of play in a playground could result in serious injury or death. Let the kids play outside. And don't force them to put a coat in cold weather if they don't want to! Let them decide!