Ice baths may not be easy for many people, but it can quickly relieve pain and inflammation after exercise. Studies have shown that ice bath is also one of the easiest and quickest ways to improve people's immunity.
Ice baths are used by tons of professional athletes, especially those who are involved in high intensity sports like football and basketball. It's unlikely they do anything for healing, and I'm with the skeptic above that they do anything for immunity, but they allow players to get back on the field quickly despite the tremendous amount of soreness that follows football collisions and basketball players hitting the floor repeatedly. Ice is only anti-inflammatory for new inflammation -- after time passes it doesn't work anymore -- but pro athletes do things we can't imagine doing and do it at great speed while running into one another, and the soreness really is painful. But you know, they also get painkilling injections and all sorts of other treatment average people can't afford. I'd be surprised if your kids needed it for anything, they're kids and recover quickly unless they are running into one another a lot. They're also a lot smaller and less muscular and a lot slower than high level athletes.