Well, you got me confused there, that's for sure. To be frank I get the B-Game aesthetic you're going for, and I like it, but in some places I'm not sure if you really intended for this aspect to get wrong or if you just hoped that your aesthetic would just make it okay.
I'll admit, I never managed to find the key. I played for a long time then gave up, then started it back up, redid everything with the armchair thing you said, then still couldn't progress, then the game crashed.
In short, I really like your aesthetic and your mood. It was a good idea for a game, but aside from the fact it's snowing outside it doesn't have much to do with the theme of coldness. The cold is merely a detail in the story and it doesn't seem that important in the core of the game itself. The core is just this silly tavern and the intentional B-game style and abstract reasoning.