SPOILERS, people. Seriously.
When I first ventured into Internet discussions of the books (which was pretty late in the game, probably close to the publication of Feast) I was surprised to find sentiments along the lines of “OMG Robb was my hero I loved him so much I can’t believe they killed him,” because to me Robb was an underdeveloped character interesting mainly for the way in which he was used as the site of the author’s toying with fantasy tropes (most significantly in the Red Wedding). Over time, I came to believe that the author had in a way tricked these readers into creating the “heroic” “character” of Robb in their own minds, taking advantage of the training they’d absorbed from other fantasy novels — and that this was one of the most interesting artistic accomplishments of the book.
So, I’m keeping track of what is actually said about Robb Stark, to see if the balance of the evidence supports my theory.
In this chapter, we learn that physically, Robb is “big and broad … with … fair skin, red-brown hair, and blue eyes.” (The later characteristics are inherited from his mother, Catelyn Stark nee Tully.)
Robb decides (it’s not clear how) that Gared “died bravely,” and can’t be bothered to even consider Jon’s observations to the contrary: his brain has already moved on to the more pressing matter of impromptu horse-racing.
Robb wants to please his father, for example by noticing the cause of the mother direwolf’s death. (To be fair, we only know that Bran believes this is Robb’s motive, but it hardly seems implausible.)
Robb “stubbornly” resists the older men’s conclusion that the direwolf puppies must be killed, and is imaginative enough to come up with the idea of feeding them milk from a dog that recently had a small litter.
Overall, Robb is depicted as a typical teenage boy: likes showing off his athletic prowess, dislikes killing puppies, wants daddy’s approval. His rude dismissal of his “friend” Jon (a person he would have been taught, at least by his mother, to view as his social inferior) shows him in a slightly more unflattering light, but only slightly — it may reflect his teenage distractibility and desire to get on with more fun activities (horse racing) as much or more than it reflects disregard for Jon’s opinions. Jon’s super-menschy behavior in giving up his chance at a direwolf pup does make him look callow by comparison, though.