Not all costumes will be available cross-platform at launch, and neither Assassin's Creed costumes nor the April Fools Fragrance costume will be available on Karting, but the rest of the DLC will eventually come to all four games.
Since dressing Sackboy up as a Disney princess or indie darling is very nearly as much fun as actually playing a LittleBigPlanet game, we'd imagine this news would be music to the ears of anyone whose nights are filled with costume changes, accessorizing and Ben & Jerry's. Not that we would have any personal, first-hand knowledge of that sort of thing. Nope.
Sony PlayStation 3 (late 2012)