So erm, when I played the square-level where, after completion, I would get a new snowman. There's a bug where if I leave the level I get the new snowman anyway.
Reply: It was in mid-battle and I left the game so I could restart the level and choose a new set of snowmen (and get more snow). I used the pause menu to leave the game and afterwards I somehow got the teleporter snowman. Then, I tried to do the same thing but it didn't work.