It really needs that song you recommended for the full effect. The goofy little iceberg with its adorable face just pairs so well with the song that the game would seriously be missing something without it. As it's not part of the game itself, I'm afraid people will miss it.
Otherwise, it's a good execution of a cute idea. The second game feels unnecessary, but including it doesn't hurt anything.
It made me smile, so you made at least one person's day a little better with this.