Freezeen Island is the first world of Mario 3D World. It is where Freezeen Castle is, and where most citizens live. Iggy Koopa took it over.
The Frozen Plains
The Frozen Plains are the equivalent of a desert in the Freezeen Kingdom. It's across a bridge from Freezeen Island, but this bridge was destroyed by Bowser- fortunately, once Iggy is defeated, it comes back. Morton Koopa Jr. took it over.
Ice Cream Cavern
Ice Cream Cavern is a cave inside Yogurt Mountain. According to the manual, several miners dig through this cavern to find jewels. Lemmy Koopa took it over.
The Snowy Paradise
The Snowy Paradise is a very snowy area on top of a "tall, tall mountain", probably Yogurt Mountain. According to the manual, kids hang out here. Dragonia Koopa took it over.
Yogurt Mountain is a very tall mountain in the Frozen Plains. It towers over the entire kingdom. Oddly enough, it is actually two mountains connected with a bridge. The bridge is over Milkshake Lake, which is actually part of this world, despite having it's own world too. Ludwig von Koopa took it over.
Milkshake Lake is a wide lake separating the Frozen Plains from the Icy Woods. It is usually crossed by a long, long bridge, but this was destroyed mostly by Bowser on his conquest. Mario and his friends use what's left of this bridge throughout the game. Ellen D. Koopa took it over.
The Icy Woods are a large forest on their own little island in the Freezeen Kingdom. It is said to be the home of scary enemies in the manual, but no "ghost house" enemies appear, oddly enough. Ludwig von Koopa took it over.
The Star Kingdom is an area over top of the Freezeen Kingdom- it is the night sky, pretty much. It is the final world of the game. Dry Bowser took it over.
Wendy, Lavora and Bowser each created their own hideouts- Wendy's Chocolate Paradise, Lavora's Ghost Ship and Bowser's Lava Paradise. Each of these areas sunk away at the end of the game.