I think the babies grow up to be those special kind of walkers that can also turn dead people into walkers, like the one that Jon killed and then destroyed all the walkers that were connected to that guy when he died. Why else would he need living babies that he would make a deal with that 1 guy that lived behind the wall?
It's the only thing that makes sense. The White Walkers still grow, still breath, and are still alive. They just shatter into tiny ice cubes when hit with Valerian steel. So the dragon is now a White Walker. He's gonna make a lot of cubes when someone hits him with one of the many weapons out there that can kill it. Maybe Sam will surprise us and kill it with the Tarly sword.