Of the omitted, I think both Django Unchained and The Master would have been worthy entrants, for stylized wear that reflects these films' time periods while also tapping into the artifice inherent in these movies' looks.
I pretty much rule out both Snow White movies right away. The royal wear on Theron and Stewart in Snow White and the Huntsman was eye-catching enough that this nomination isn't shocking, but a lot of it struck me as fairly generic fantasy wear, in a lousy, witless movie.
Mirror Mirror, a far worse movie, has some more original designs -- the ornate animal-themed costumes at the ball are quite clever -- and I guess it's nice that Eiko Ishioka received this final nomination. But the movie is far too silly to garner serious votes, and I assume plenty of people will cast ballots without having even seen it.
I think the remaining three candidates all have a shot at the prize.
Lincoln's costumes are really impressive -- the weathered, lived-in look of the clothes makes it seem like the characters have been wearing these outfits for years. And the task of costuming such a big cast, from politicians to wives to military commanders to servants, will not be lost on voters. But in terms of winning this thing, I think the movie has a drawback: a lack of too many female characters, and by extension, the type of ornate gowns that tend to lead films to victory here. Yes, Sally Field's costumes are terrific, but aside from her there isn't a ton of glamor on display. I think overall, the costumes might end up being too drab to win.
I've pretty much been a grouch about Les Mis, but I will acknowledge that the costumes were one of its prime elements of achievement. Like Lincoln, the film covers a lot of ground in the clothes department, from the poor factory workers to the colorful prostitutes to the refined wear of the upper class to the striking colors of the police. And the outfits worn by Carter and Cohen were pretty crazy and eye-catching. I definitely think it's in the running, and if the movie seemed stronger overall, I might predict it. But plenty of the costumes aren't what you'd call "beautiful" -- there's a lot of grime in this movie -- and in the end...
...I think voters will equate Best Costume Design with most luxurious dresses, and Anna Karenina will prevail. I had a lot of problems with the concept and execution of this movie. But it's hard to deny the visual wow of individual elements, especially as Keira Knightley dons one gorgeous frock after another in this film. Lincoln and Les Mis may have Best Picture pull, but voters have proven that in this category, they'll look beyond films in the major races and often choose the most elaborate candidates regardless (Elizabeth: The Golden Age, Marie Antoinette, The Duchess). And Anna Karenina has a pretty solid number of tech nominations, signaling that voters in numerous branches were quite taken by the visual look of the film. A win by Lincoln or Les Mis wouldn't shock me, but I think I'll be placing my bet on Anna Karenina.