If the navigator says it's permitted, it's permitted. I would imagine that they should be accompanied by an adult, but I'm not sure about that. There is also a walking track on deck 4, open to all, and a sports are on deck 10 with basketball courts that anyone can use as long as the kids programs aren't on them.
The workout area is a little small (remember you are on a ship), but it's nicely equipped.
Enjoy!