I agree with darkling_menace about Princess Cadance being like Ariel. This Day Aria really did seem like Vanessa's song in the The Little Mermaid. However, I also think she is like Rapunzel because it was Cadance's love that saved Shining Armor and Equestria. Just like how Rapunzel's love for Eugene allowed her tear to heal him. Also the colors of Cadance match the colors of Rapunzel's purple dress.
1.Aurora because this roll on her hair is similar to Cadence's.
2.Snow-White because of her gentle personality
3.She always seemed to be Cinderella type to me
I don't know about other princesses though