It was a great idea to limit what the player can do to two things! I'm really impressed by how well the mechanics fit the theme and how well it still works as a mechanic.
The things you can do are very simple, yet the ways in which you can use them are super varied and creative. It involves thinking about what is possible, and it involves executing tricky combinations of the two inputs like freezing to turn at a corner. It seems like this game applies the design philosophies you hear about in video essays like those from Mark Brown's GMTK. Well done!
The music fits (although you didn't make it) and you put some real effort to also theme the whole game about ice and freezing, with the penguin and the snow effects and the backgrounds. I also like how the penguin freezes at the goal area and again recalls the theme. Talking about it, you did so well to make the player character so expressive, I love the flapping as well as the freezing, and love the sunglasses!
The only criticism I have is that sometimes you feel a bit tricked, like when you go on a platform and you don't move with it like in most platformers. The levels with red ice behind the goal area also kind of fall into this category, it's very hard for those to get the timing of freezing right. Though I did it after a while, it didn't feel as fun as the rest. I would also suggest adding some checkpoints so if you brave one difficult stretch, you can tackle the next one in peace. But this is maybe a bit beyond the scope of a short game jam, and it's just as great to have more levels, which you made a lot of! Totally worht spending the time on that.
Overall, a phenomenal game that integrates the theme at every step, is fun to play and offers lots of content for a jam game, especially for a solo dev.