In 2D animation, the characters are all individual drawings, so giving your character a new costume is simply a matter of designing the new costume and then drawing it on the character. 3D is different because it's much more difficult and expensive to design multiple costume changes for the characters.
But even so, costume changes for animated Disney characters is rare, and always have been, even in the 2D films. This is because we want the characters to have one iconic look that represents the way you think of the character. When I say "Snow White", you think of the character with her distinctive blue, red and yellow dress. The dress is a big part of her distinctive appearance. If she changed dresses three times during the movie, her appearance gets diluted and she loses her iconic appearance. If that were the case, you might see a sketch of her and have to look twice to figure out if it's her, based on her face....as it is now, you see the dress, and instantly your brain knows it's Snow White. End of story.
So, other than Disney princesses and princes wearing wedding clothes at the end of the movie, most of them wear the same iconic outfit all through a movie (no matter how many days the film covers....yeech).
The grossness factor is not why I'm bringing it up, though. The reason I sometimes wish we could play around with this rule is that costume design--and how it changes and evolves over a movie--can play a really important role in giving the audience an insight into what the character's mental state is and how it's shifting over the course of a movie. And that can be a powerful tool for giving the audience a glimpse into the thinking and emotions of the characters.
Live action movies, of course, do this all the time. Usually, it's done in a way that isn't obvious to the viewer and works on a subconscious level. The Star Wars films [SPOILERS AHEAD] are a good example. In the first film, Luke wears all white, which represents his simple, naive nature and his lack of experience and uncluttered moral nature. He's pure good and believes in a simple, clear version of what's right and wrong.
In the final film, Luke wears black. A big point of tension in the film is whether Luke will become evil like his Father, or remain true to his better instincts and resist the lure of the Dark Side. So it makes sense to dress him in black, both to illustrate how far he's come since his youthful days, and create tension in the audience's mind that he might follow his Father's footsteps....after all, they already dress alike!
"The Godfather" [SPOILERS ahead] is another film that I remember as having very smart costume design. I haven't seen it in years (so someone correct me if I'm wrong), but when we first see Michael, he's wearing his marine uniform. He's a returning WW2 hero, and in the huge party of people seen in the beginning, he's the only one we see wearing a uniform. He's heroic looking and stands out. He tells Kay (his girlfriend) that his family is connected with the Mafia and that he wants nothing to do with them. He's very different from them, and he doesn't like the moral compromises they've made. He's similar to Luke, in that he sees things in black and white and believes very strongly in right and wrong.
In the middle of the film, I remember him wearing a lot of black as he's forced to accept more responsibility in the business his family has created. Black is a strong, forceful color, and I don;t think it's meant to represent evil here. I think it represents Michael's belief in his own strength and how he sees himself as a force for good. He's only done what he had to do to protect his family from people who are worse than they are, and he fully intends to get his family into legitimate business and get them out of organized crime.
By the end of the film, Michael wears a grey suit and hat to represent how far he's slipped in terms of moral certainty. He's lost sight of what's right and wrong and he's become completely corrupted.
Anyway, you get the idea. I'm no expert in costume design, and I don't know of a great book or website on the topic of using costume to tell story. I wish I did; if someone knows a great resource on this subject, drop me a line. In any case, it's not hard to learn about costume design. Great film makers use it to their advantage constantly, so just look at how it's used in films that are well put together. Ask yourself why certain choices were made, and you'll see that it's not that much of a mystery how costume can help tell a story.
I've been working on my own graphic novel for several years now, and I enjoy working on it because I get to do many things that I never get to do as a storyboard artist. Costume design is one of the things that I never got much chance to do before, and I really like the challenge of coming up with clothes that help illustrate the changing mental state of each character.
Of course, there are two types of film characters: those that undergo a transformation (like Luke and Michael Corleone) and those that remain the same throughout a film and change the world around them. When I think of the latter type (the type that don't undergo a transformation), it's no surprise that those types wear the same costume throughout a film. Their mental state doesn't change, so they don't need evolving costumes to reflect that change. Characters like Mary Poppins and Indiana Jones are the first kind to come to mind when I think of that type of character, and it's probably no coincidence that they both have very iconic costumes.
Actually, if you wanted to nitpick, I guess you could say that Indiana Jones changes a little during the first film, but not in the major way that Luke and Michael Corleone do, so he doesn't require drastic costume changes. Also, Mary Poppins does change outfits in the fantasy sequences...but hopefully you get my drift.
Anyway, I'm a big believer in using every resource available to help tell stories, and I think that costume design is one area that animation has yet to fully exploit for emotional impact.