Re: fitness for a 3 yr old. just keep them outside?
I believe it is worth searching out CrossFit Kids programs in your area, watch a class or two, and talk to the coaches to see what they recommend. I don't have experience coaching kids that young, but have observed multiple different CrossFit Kids coaches. The good ones are masters at getting kids to move, have fun, and reinforce the positive movement patterns they typically already have if they are still so young.
Is 3 too young?
I don't know. But the good CrossFit Kids coaches will be able to give you some knowledgeable guidance. When our box got a great kids coach--who is also a kindergarten teacher so he is quite experienced working with young kids--the program exploded in numbers and the kids absolutely love it. I'm amazed at what he has accomplished. The kids love it, they are loud, and it looks like all fun and games for them even though they are doing lots of the same stuff you would see in our regular classes.