Of course you can play on mountain bikes! That's what they're for! My Fisher says "All work and no play is not good at all" on the headset.
Crashing - I crash more frequently on my mountain bike but get hurt less. When I crash on my road bike, it's usually spectacular and hurts a lot more. Road rash...yuk. Yes, I've done the falling over at a stoplight routine. The thing that hurts most is my PRIDE!