This is, apparently, just a small sampling of the deleted scenes that are included in the Season 3 box set (out today). It is enough to make me think they should extend each season from 10 to 12 episodes or make each episode longer. It seems like some good stuff, stuff that would make the show more true to the books, being cut.
Included in this set:
0:00 Jon and Mance (extended)
5:26 Robb, northmen and the Tullys (extended)
9:07 Tywin and Pycelle (deleted)
12:26 small council discusses the wildling threat (deleted)
13:20 jon snow does nothing of importance (deleted)
Via io9