As per the quest The Splintered Throne, you're required to collect 60 of the little buggers, and from the site, it appears that they're around a 25-50% drop rate off of all bosses except Arthas in the 25-man version of Icecrown Citadel on normal mode and a 50-100% chance off of the Heroic versions of the same bosses.
All in all, not bad. It'll still be a, well, legendary process to get your axe crafted, but at least you won't need to suffer through awful drop rates to make it happen.
Patch 3.3 is the last major patch of Wrath of the Lich King. With the new Icecrown Citadel 5-man dungeons and 10/25-man raid arriving soon, patch 3.3 will deal the final blow to Arthas. WoW.com's Guide to Patch 3.3 will keep you updated with all the latest patch news.