Do you think the north, with its history of ironborn raids and wildling invasions, would have a militia system in place? Or would that undermine the nobility? I could see the south blocking such a thing with their culture rooted in knighthood and an elite military caste. And does the pike and shield wall appear like a northern cultural thing handed down by the First Men or does it appear elsewhere?

A fyrd is not incompatible with feudalism – just ask the Anglo-Saxon earls, thanes, and kings – but the North seems to have a later feudal levy system as opposed to either the pre- or post-Alfred fyrd system.

Pikes are used elsewhere in Westeros – pikemen are mentioned in Rhaegar’s army, the pikemen of Lannisport are supposed to be well-trained, Catelyn sees tons of pikes at Renly’s camp at Bitterbridge, and on and on.

Shield walls are also mentioned elsewhere – Randyll Tarly discusses charging a shield wall at Storm’s End, the Ironborn use it at Torrhen’s Square, Stannis’ infantry try to form them when attacked on the southern bank of the Blackwater, the Unsullied fight in shield wall, Bennis the Brown tries to teach Ser Eustace’s peasants to fight in shield wall, etc.