At the Wall, things are going better. Snow is sparring cheerfully and telling his fellow recruits how to fight. You, move more. You, move less. That sort of thing. Everyone's getting along well, so I can only assume that everyone at the Wall is going to be all right. Forever. Nothing could possibly go wrong.
Tyrion is still hobnobbing with the leadership of the Wall, He says that he's seen eight winters, then corrects that to nine. For a second, it seems like he's a lot younger than he looks (and that scene with the whores seems wildly inappropriate), but then he adds that the winter of his birth was three years long, and that this summer has lasted nine. What? I don't understand this cosmology at all, but I guess it helps give some context for the Starks going around saying "Winter is coming" all the time. It's a more useful thing to say when the last winter could be as much as a decade ago. An aged gentleman does, in fact, say that winter is coming. Wildlings have seen White Walkers, but Tyrion airily mocks this (it's very nearly persiflage!), saying that fisherman claim to see mermaids. The aged gentleman continues to predict doom. There are less than a thousand in the Night's Watch, and they're all that stand between the realm and "what lies beyond." So they would like Tyrion to return to King's Landing and tell his sister that the Wall needs more people. My guess is that she'll be okay with imprisoning people, as long as she gets to put a few of the heads on pikes now and then.
Daenerys and Drogo are entwined in their tent. There are candles, dragon eggs, and a fire. She tells him she knows that it's a boy, and they kiss. Looks like everything's going fine here, too!
Tyrion is, in fact, pissing of the top of the Wall, just like he said he would. He's a man of his word! Snow waits for him to be done, then tells him that he's sorry to see him leave. "It's either me or this cold, and it doesn't seem to be going anywhere." Snow asks Tyrion to tell Bran he'll miss him. Tyrion is not overflowing with the milk of human kindness: "If you're going to be a cripple, it's better to be a rich cripple." They part, with Tyrion calling Jon "Lord Snow," but I don't think he means it in a mean way.
Arya enters a room that's occupied by a bushy-haired foreign person named Syrio Forel. He's basically Italian, but you have to translate that into this world, so I don't know what the local name is. Did you see Topsy Turvy? Do you remember the dance master? That's kind of what this guy is like. And, in fact, he is allegedly giving Arya "dancing lessons." He starts by calling her a boy and throwing a wooden sword at her. She drops it, but he tells her that tomorrow, she'll catch it. She whines that it's too heavy to use it one-handed, but, says Syrio, it will make her strong. He makes her turn sideways and praises her skinniness since it presents less of a target. He adjusts her grip. "The steel must be part of your arm! Can you drop part of your arm?" I want to emphasize this: although obviously none of this show is set in the real world, he is extravagantly foreign. She points out that she's a girl, not a boy, but he doesn't care: "Boy, girl. You are a sword. " While trying to refine her grip, he tells her, "You are holding..." And she finishes the sentence, "...a needle!" "Just so." This style of swordfighting is different from the usual Westeros brutality; he calls it "the water dance." He's also got a water-based theory: "All men are made of water. Did you know this? If you pierce them, the water leaks out and they die." He tells her to try to strike her. She swings wildly, and he does fancy sword things in response to get out of the way. She is undeterred. He keeps tapping her with the sword, telling her she's dead over and over again. She doesn't stop, but she does lose her sword. And the next time he throws the sword, she catches it. She's very motivated, even though she keeps dying. Ned looks in and as he watches, the sounds of the wooden swords are replaced by steel on steel. He looks more serious and he's either contemplating his little girl getting into real sword fights or the many life-or-death fights he's been in himself. Or both. Or it's possible they just used the wrong sound effects, I guess.