Yeah, just inferring from what they showed last night--the corpses only rose after the white dude did some magicky thing with his arms.
With the baby in the previous season, I think we saw 12 of those guys around the altar, and the one--the same crowned dude that made the zombies in this episode--performing the actual ritual?
So putting some things together, perhaps they need a full council of whites--so 12--to create a new white one, and perhaps only one of them has the full power to make a zombie army, or even make a new white one? But it looks like snow and ice was all it took at the beginning of that siege, but we didn't really see what happened. Could be that they created the ice storm, killed all outside the gate, and performed magic zombie army ritual off camera.
I think there were a lot of clues in place as to how they work, how they can be defeated, but nothing is certain.