The ice palace was an extension of Elsa, it reacted to her emotions very noticeably throughout the film. So when Anna knocks on this door it simply reacts to Elsa’s unconscious feelings. So of course it opened to Anna’s knock. Because that was all Elsa wanted to do for 13 years.
Love is an open door.
The ice palace door has a heart on it
(Source: kpfun, via vorixcia-dix)