Additional things that still aren't clear. It's not clear what kind of ritual is needed or what it's range might be in order to raise people as zombies. Or whether it's more or less automatic. (It certainly isn't automatic south of the Wall - at least not at this point.) It's also unclear whether the intelligent "Others" have their own bodies or are somehow possessing the bodies of the living. The whole thing is still uncatalogued (and probably scarier as a result of that).
When they created the wall, they instilled some sort of magic into its core. It acts as a giant stop gap on not just flesh, but spells. SPOILER: ( Remember when Snow went back over the wall, and he couldn't sense Ghost anymore? That was because of the wall blocking his warg senses. )