Catelyn has her own personal spa in Winterfell's hot springs, but Eddard rarely joins her because he is the personification of winter, right down to his business-like performance in bed. We learn a bit about Lord Stark''s history and why he's so serious: it's hard to smile when your sister, father, and brother are all dead before their time. Ned sounds like he really needs a vacation. He needs to enjoy his southern hottie wife and badass children, especially after a long day's work of executing deserters and refraining from laughing.
Via secret letter, we learn that Queen Lannister murdered Jon Arryn. I had to look up who this guy was in the appendix*. Lord Arryn was the former King's Hand, and thus his death is why King Bob came north to offer the position to Ned. To get to the bottom of the murder, Ned decides to accept the King's offer. Eddard also decrees that Catelyn must stay in the north. How many Jon and Jane Snows will he bring back with him this time? His affair makes sense though, because someone who is so intense and emotionless all the time must be prone to sudden and major lapses in discipline. Without this flaw, I would have predicted that Martin would soon reveal that Eddard Stark is actually a robot. Ned decides to take his daughters to court, while Robb and Bran stay at Winterfell with Catelyn and Jon Snow goes north to fight Zombie Waymar.
Lastly, we learn that Catelyn hates Jon Snow, and it's hard to blame her. Jon is a constant symbol of her husband's unfaithfulness, he's got an annoying matyr complex, and he makes friends with ugly Lannisters while getting drunk at Winterfell social events.
* I laughed out loud when I saw that the Arryn motto is "as high as honor" and they have a bastard girl named "Mya Stoned".
Arya's chapter is easily my favorite so far. Her personality is perceptive and hilarious, delivering several quality zingers throughout the chapter. She has some serious Ashlee Simpson-esque jealousy going on, but only because she is too young to see that her skills in math and horseback riding are far more awesome than Sansa's dancing, singing, and sewing. She named her wolf appropriately (Sansa named a wolf "Lady", what the hell), she treats Jon with respect, and she wants to go fight with the boys. I can't think of anything I dislike about her.
We also learn that Prince Joffrey predictably sucks at swordfighting and that he and his men are huge assholes. This doesn't bode well for Sansa, but it could be worse -- at least he isn't a gigantic Khal three times her age or an over-the-hill King who is still in love with a dead girl. Ned and Catelyn seem to have the only healthy, loving relationship, and even theirs is characterized by duty and adultery.