You will be unable to learn a new one. In a bug first noticed by new DK's wanting to craft an epic to bring to Northrend with them and later confirmed by other characters, if you go to Winterspring to pick up a weaponsmithing specialization the three NPC's do not give it to you. As a swordsmith myself, I'm not willing to unlearn my profession to test it out, it does seem very strongly corroborated at this point.
While this isn't a major issue to those of us at 80 as there are currently no top end weapons that require one of the three specializations, it not only prevents these leveling characters from making the epic weapons it could prevent a character who currently is an armorsmith from being able to trade specializations. It's certainly not the end of the world for most of us, just don't try and retrain until it's fixed, but it's got to be a bummer for the people who intended to have a fun new toy in Northrend and will instead be staring at a pile of mats they won't have any use for.