To complete the dream world, you first need to complete the initial maze. Once that's done, you can exit through the south gate (which is in the room you started the game in, in the southwest corner of the maze). This will take you to a set of three rooms meant to teach you about the dream world. When you fall asleep on a bench, the completed snowmen in the "real world" become single size-3 snowballs in the dream world, and rolling them reduces their size and leaves behind a trail (which other snowballs can roll on without becoming smaller). Stack one snowball of each size on top of each other to build a "meta-snowman" which will quickly flash between the accessories of the three snowmen that you used to make it.
You can now move south to a new maze. Your goal is to re-solve the rooms in this maze such that there are groups of three snowmen close enough to each other for you to build meta-snowmen out of them. Once a room has had its snowmen used to build meta-snowmen, the floor will change color in the dream world. In most cases, the tricky part here is deciding which rooms should pair with which others. A good tactic is to start at the southwest corner and solve the few sets of three that are forced to be grouped together. The northwest corner and middle-south parts of the maze can also be solved without putting too much thought into deciding which rooms pair with which others, as long as you start from the southwest corner and work out from there.
The northeast corner is trickier. I don't think I can describe with words how they group together very well, so I suggest looking for a guide on YouTube if you're having trouble. A few hints:
* The room with two snowmen in the far southeast corner pairs with the witch-themed snowman immediately north.
* The room with three snowmen doesn't pair with any other room; you can use all three of those snowmen together to make a meta-snowman.
* The "final room" (the one which had the exit in the initial maze) should have one snowman in the southwest corner and one snowman in the northeast corner. The one in the southwest corner pairs with the room directly west and directly southwest. The one in the northeast corner pairs with the two snowmen in the room to the east, which should both be on the north side of the little outcropping that one of the large snowballs spawns in, with one snowman as far west as possible and the other directly east of it.
I don't know if the way I solved the dream world puzzles is the only way to solve them, but this worked for me. Taking those three hints into account I don't think there's too much ambiguity left in how you should combine the remaining rooms.