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Note the repeated use of door imagery throughout Frozen. It begins in "Do You Want to Build a Snowman", with Anna constantly asking her sister to come out and play and to "come out the door", before immediately continuing in the next song, "For the First Time in Forever" in which Anna sings about how, "for the first time in forever" the castle doors and gates will be opened. Therefore, when given the opportunity to sing about true love, it is no surprise that Anna chooses to perform "Love is an Open Door", since she associates love with doors. It must be concluded as a result that Anna feels that Elsa does not love her, and in fact, rejects her, since her door is always closed to Anna.
On the other hand, Elsa does not associate love with doors, but rather with heat. It is her cold based powers that cause her to be cut off from the world, and therefore she links the two ideas in her mind. It is no accident that "Let it Go" begins with the line "a kingdom of ice-olation". Perhaps the largest proof for this association however, is Olaf. Olaf is created by Elsa, and his personality is based on Elsa's childhood memories; his use of the phrase "the sky's awake", his introduction being that "My name is Olaf and I like warm hugs", and even his appearance being identical to that of the snowman Elsa and Anna built when they were young, all show that Olaf is not a unique and independent being, but rather an extension of Elsa's psyche. He is an anthropomorphic representation of her subconscious, and her heart's desires. And, therefore, when Olaf sings, he is showing Elsa's true feelings; and the song that Olaf chooses to sing is "In Summer", extolling the virtues of heat.
When Elsa sings the line in "Let it Go" of "the cold never bothered me anyway" it is not literal; she is not discussing yet another winter-related superpower of her magic. It is the same refrain that everyone tells themselves when they are denied; "I never wanted to be friends with her anyway. I didn't want that stupid bike in the first place". The cold to Elsa represents being forced to be alone, after the very public way in which everyone freaked out upon discovering her powers, and in "Let it Go" she is lying to herself that it doesn't matter, that she doesn't care that she is forced out of her own kingdom and to live alone in the mountains.
On the other hand, Elsa does not associate love with doors, but rather with heat. It is her cold based powers that cause her to be cut off from the world, and therefore she links the two ideas in her mind. It is no accident that "Let it Go" begins with the line "a kingdom of ice-olation". Perhaps the largest proof for this association however, is Olaf. Olaf is created by Elsa, and his personality is based on Elsa's childhood memories; his use of the phrase "the sky's awake", his introduction being that "My name is Olaf and I like warm hugs", and even his appearance being identical to that of the snowman Elsa and Anna built when they were young, all show that Olaf is not a unique and independent being, but rather an extension of Elsa's psyche. He is an anthropomorphic representation of her subconscious, and her heart's desires. And, therefore, when Olaf sings, he is showing Elsa's true feelings; and the song that Olaf chooses to sing is "In Summer", extolling the virtues of heat.
When Elsa sings the line in "Let it Go" of "the cold never bothered me anyway" it is not literal; she is not discussing yet another winter-related superpower of her magic. It is the same refrain that everyone tells themselves when they are denied; "I never wanted to be friends with her anyway. I didn't want that stupid bike in the first place". The cold to Elsa represents being forced to be alone, after the very public way in which everyone freaked out upon discovering her powers, and in "Let it Go" she is lying to herself that it doesn't matter, that she doesn't care that she is forced out of her own kingdom and to live alone in the mountains.
