The episode's title is a parody of Three Men and a Baby.
Differences from Snow White and The Seven Dwarfs
It is very likely the way the story was told it was parodied after Disney's Snow White. However Lisa said it was from the fairy tale. Here are the differences.
In the movie Doc is the leader of the Dwarfs. However in this version Doctor Hibbert is in back and Crabby/Moe is the leader.
In the movie and original, the object that tells the Queen who is the most beautiful is a mirror. But this object is an HD-TV.
One of the biggest differences is Snow White's appearance. In the movie she is 14 and by birth a princess. She has black hair and is wearing a yellow and blue dress. But this version has her as a peasant and not related to the Queen. She is also about 12 and is very different from the movie.
In the movie and original, the person hired to get Snow White's heart gives the heart of a pig. But in this version the Queen wants her heart in one box and her body in another. Also she is not given the heart of anything. It's unknown what became of Huntsman Willie.
Marge complained that Homer killed everyone in their costumes, however Doctor Hibbert wasn't.