How did frisk feel about charlotts climb

I could only imagine that Frisk did it because they were curious or adventurous in spirit. Or it could just be another plot hole.

It certainly can put the wrong idea into the player's head when Frisk can choose to stay with Toriel at the end considering that, at the beginning, you're expected to try to leave the ruins (thus leading to her comment about it, should you choose to stay with her.)

That being said, Frisk's backstory is, most likely, whatever you want it to be - abused child, adventurous spirit, heck, maybe it was just spur of the moment or divine intervention. The backstory is up to our imagination...probably.