The Winter Dream occurs on the last day of Winter, if you pass up going to the festival on that day and just go to bed. It's a completely random event; you get one of several dream sequences, and you have no control over which one you get or whom you attend it with. It's just a fun little cutscene; it has no effect on your game whatsoever, no one will have raised affection for you if you get a sequence with him or her in it, etc.