[Hey even if Elsa would accidentally hurt Korra with that magic, she could just bend it away from her body right now. Probably. How does magic vs bending even work, no need to find out today.

She's probably used to hugging people, who are not very improved with their powers anyway considering she's from the world where ice/water and other element magic is completely normal and she was locked up into a place where new waterbenders are born and grow up.

Korra smiles when Elsa hugs her back. She accepts all kind of hugs, really, and she's just so glad that Elsa doesn't push away. Sure, this is probably really weird for her, suddenly being hugged by someone who she doesn't know really well, but Korra on the other hand is an extremely affectionate person, who generally hugs almost every good acquiantance without hesitation.

So her hug is not stiff at all. She's just very calm and trying to be as soothing as possible to make Elsa relax there.]

Anytime, really. If you ever want to talk more about it or anything else, the inbox of my gear is always open in case I'm not around on the network.