Physical Description and Attributes
The Snowman's appearance most likely resembles a typical snowman built by real snow. However, it appears this one in particular has been given life, and is able to now interact with the physical world. In addition, this Snowman must be hostile to humans in someway if it is kept in the Facility and was a contestant for sacrificing the victims of the Cabin. Because the Snowman is not shown at any point during the film or even in behind the scenes, any noticeable features and behavior remains a mystery. How the Snowman was brought to life or where he was created is completely unknown, but its very possible that some sort of dark magic was used with the intent of causing harm to others with a seemingly harmless and friendly thing.
The item that summons the Snowman is unknown. Possibilities include the components used in creating a typical snowman such as a carrot (used for his nose) coal (buttons) or sticks (arms). A snow globe is another possibility.
It is not seen during the Purge or anywhere else in the film as mentioned earlier. He is not even seen in behind the scenes footage or in the visual companion book. This leads us to believe he was only put here as a joke or filler-monster.
Possibly a reference to Jack Frost , the Goosebumps book Beware, the Snowman, or perhaps even the Snowman from the Time Splitters series. Another possible reference could be to the popular YouTube prankster ICEMAN, who wears a snowman costume and scares people passing by as a prank.