I have to agree with the theory that they become White Walkers. There is no evidence for it, bu there is counter evidence for its counter evidence.
The Night King. A thousand years ago - the description could slowly have changed of his bride. His bride might even have been a Child of the Forest - give enough time, and people will change the details. See it like natural selection. Each re-telling changes a detail. If the change captivates the audience, it gets passed on.
And there are no female White Walkers shown so far. I suspect that, yes, they sometimes take living prisoners (Craster's sacrifices) to become them.
And their motives. What could their motives be?