cool puzzle game, cute story and graphics

Not a bad game, short but a very heartfelt cutesy story attached. neato

I think it's great. Somewhat challenging (but not too hard) puzzles, the gameplay which evolves as the game progresses, just as the difficulty – with an interesting art style which matches the current mood and a neat little story, too. Reminds me of "The Company of Myself".

As for improvements, I think it could be made more powerful by changing the background music at certain points (it plays the same cheerful loop both during the "warm, we're together" levels and the "cold, pushing back" levels). And when the story finishes, "And she forgave me." with an instant cut to menu feels a bit flat (because it doesn't top anything which came before, it merely returns the story to the state it was a few levels ago).
The movement can be a bit confusing, too. The characters move continuously, but you're expected to tap the key only once (holding doesn't work) which is counter-intuitive. I think moving on a grid, as you did, is the better option, but in my opinion, it would work better if the characters instantly snapped to their new position instead of slowly walking there.

Also, when choosing the vertical resolution in Project System, you need to add the height of the footer, too (unless you pick the "Minimal" WebGL Template in Unity), otherwise your game window is going to be cut off at the top and at the bottom.

But other than that, well done!