So I know I have a tendency to overanalyze everything, but I couldn’t help noticing something in Frozen.

Olaf was there in the beginning when Elsa accidentally struck Anna with her powers. That means, theoretically, that Anna getting hurt was the last thing Olaf registered before he collapsed into a pile of snow.

Olaf then was rebuilt by Elsa during the fabulous Let It Go sequence without her knowing he was alive. He most likely walked away and wandered around for a while. However, I am convinced he was searching for Anna the entire time to see if she was okay.

He is next seen bumping into Anna and Kristoff, noticeably not taking a liking to Kristoff. This makes it seem like maybe he didn’t trust anyone around Anna, seeing as she was previously hurt by one of the people she would always trust.

Throughout the rest of the movie Olaf is constantly saving Anna from any harm whatsoever.

When he took on Marshmallow to let them escape,

When they were convinced Kristoff was crazy and possibly dangerous so he wanted her to get away,

When he risked melting to make sure Anna was warm, going far enough to say “Some people are worth melting for”, meaning he would have no problem sacrificing himself for her well-being.

When he did everything he could to help Anna escape the freezing castle,

And at the end when he was totally fine with dying because Anna was finally safe with Elsa and Kristoff. Even though he was saved by his own personal flurry, he was happy to die now that he managed to keep Anna safe during everything.

Even something as small as keeping Anna from falling during ice skating.

So my headcanon is that Olaf’s mission during Frozen was to do anything possible to keep Anna from harm ever since the last thing he saw before crumbling was Anna being in danger and him not being able to help her.