With nothing in the way of reading, and little in the way of dialogue in the cartoons themselves, the barrier for entry is very low here, and even the littlest ones should be able to enjoy at least watching the shows (which are actually pretty good!) In terms of gameplay, there really isn't very much to it, and everything is well explained in game. Perhaps the only real issue here is that in the "race" mode cartoons, which basically throw actions at you back-to-back, it often ends up simply distracting you from the episode itself. You don't have time to watch when you're so busy posing!
In fact, perhaps the only real barrier here is Kinect. The motion sensing camera struggles picking up people who are too short (and often struggles picking up those who are taller too), with the limit being around 3ft 3in for the original Kinect sensor (we haven't been able to find anything about minimum heights for the Playstation Camera or Xbox One Kinect). It should also be mentioned that the menu is a little bit tricky to navigate (although, thankfully, you can use a controller for that), so younger kids will likely need some help off Mom and Dad to get going, but once they're in, they should be good to go. It's also worth keeping in mind that this is one of those games that comes with a season pass. While there are 20 episodes on the disc, there are another 15 that can be downloaded off the console's store - so be prepared for some pestering if your kids discover them!