This is a really good take on the theme. It's really commendable that you managed to make a short narrative intro to give more context to your game, and even added an FTUE! I think details like these make the game feel really polished.
The actual gameplay is fun too, esp with new mechanics. I think that the ice melting speed could be a bit slower when there's a new mech being introduced so the player has some more time to read and understand what's happening. It took me some time to get a grasp on the controls and remember who is who, and which number to press for which penguin. I found this a bit difficult when Tux's ability was being introduced. By the time I remembered to press 2, then E, then Q, the ice was already nearly broken. But I guess it's something you learn through failure?
Adding the spacebar as an input would really help with making the controls easier.
It would also be nice if the game could remember the last character I had selected. It starts to feel tedious to select a character each time a level starts, because I'm just automatically trying to move the penguins before selecting them.
These are subjective, of course.
Overall, I just LOVE the art. The SFX when toggling between penguins, or when they reach the goal is also really cute.
Well done!