Snow White appears as one of the fairy tale creatures banished to Shrek's Swamp by Lord Farquaad. She is sleeping in her glass coffin, handled by the 7 Dwarves. Later the Magic Mirror also gave her as an option to be the princess of Lord Farquaad. She is also one of the princesses who attempts to catch the bouquet, but Dragon gets it instead.
Shrek The Third
Snow White appears in Shrek the Third now with a major role. She is one of the princesses in Fiona's princesses circle along with: Cinderella, Sleeping Beauty, Doris, Rapunzel and Dragon. Later when Far Far Away was attacked by the villains (led by Prince Charming), she along with the princesses escaped though a secret tunnel. After Rapunzel betrayed them they eventually escaped from the prison with the help of Queen Lillian and prepared for battle. Snow White is the one who knocks out the guards of the castle Steve and Ed with the help of the animal creatures by singing "Immigrant Song" by Led Zeppelin. She was then later seen at the end when they turned the bad guys to good guys.
Unlike her traditional characterization, Snow White is portrayed as being arrogant, acerbic, sarcastic, opinionated, stubborn, stuck-up, and lazy. She gives Fiona one of her dwarves as a baby shower gift, and states that all of the Princesses (with an exception to Doris) were all fair maidens. She seemingly resents Rapunzel, stating "Rapunzel, Rapunzel, let down thy golden extensions" as they walked in the sewers to escape.
Despite this, she is genuinely loyal and plays a major role in the fight against Prince Charming.