Is swinging on a swinging good exercise?

Not really: There is minimal exertion required to set in motion a swing. It's a small amount of exercise, but not a significant amount.

Swinging: Not necessarily improving cardiovascular or muscle strength unless you are doing the pushing. But, it is fun and if you at the play ground also walking, hanging from monkey bars, climbing etc it can be good exercise. Even at 37 there is very little more child like and fun than swinging on a swing. Enjoy!