Clearly, we cannot start this section without referencing Lost. And if you have no idea what we mean, go ahead and watch all six seasons immediately. We'll wait.
Okay, you back? Here we go. We don't really know anything about the Others and that's what scares us. They are the monsters of the cold north. Old Nan remembers stories about how they almost killed everyone in the Seven Kingdoms, and who knows if she's right.
But the Others haven't been around in many hundreds of years, so today, people just use "the Others" as a sort of curse, without any sense of how dangerous or scary they might be. For example, a baker tells Arya, "The Others take your pigeon" (66 Arya 5.8). But surely he doesn't really want the Others to show up in King's Landing, take her pigeon, and kill everyone there, which is what they would do. Clearly, this man has never heard Old Nan's stories about the Others:
"Cold and dead they were, and they hated iron and fire and the touch of the sun, and every living creature with hot blood in its veins. Holdfasts and cities and kingdoms of men all fell before them, as they moved south on pale dead horses, leading hosts of the slain. They fed their dead servants on the flesh of human children..." (53 Jon 7.59).
So, if they want a pigeon, the Others can get it themselves, thank you very much. It is important to note that we never actually see the Others in this book, except in the Prologue, where they kill a few Night's Watchmen that we don't really care about. (Hey, it's the first chapter, we weren't into it yet!)
We do see a few of the Others' soldiers, the wights. These are reanimated corpses of the dead who go out to kill people. (Yes, they're zombies.)
Here's what we see of them: Ser Waymar Royce is turned into a wight in the Prologue and kills Will; Jon faces a wight who used to be Othor, a man of the Night's Watch (53 Jon 7); and another wight manages to kill five Night's Watch guards (61 Jon 8). If the wights are that dangerous, just imagine how dangerous the Others really are.
Like dragons and direwolves, a wight is not something that Martin invented. (Sorry to disappoint!) Although the term "wight" used to just mean "person," fantasy authors in the twentieth century, such as J.R.R. Tolkien, have used it to mean some sort of undead monster. So really, when we call the wights "snow zombies," we're not so far off.