Any snowman that has no mouth or who's mouth is shaped in such a way that it makes the snowman look serious, is a serious snowman.
A Serious Snowman is a snowman that you will not want to venture too close too. The serious snowmen are notorious for being overly violent and territorial, especially towards smiling snowmen.
note: Any normal snowman can be converted into a Serious Snowman at any point in its lifespan. There have been occurrences where entire neighborhoods of snowmen have been converted into Serious Snowmen by radical snowman rights activists.
Justin : “Hey lets go make snow angels in that yard across the street!”
A.J. : “I don't think thats a good idea...”
Justin : “Why not?”
A.J. : “Because thats a Serious Snowman in that guys yard, see how his coal mouth is so serious looking. And besides, it would be hard to make snow angels with all those mutilated snowmen corpses littering the yard.”
Justin : "Well what about that other yard over there."
A.J. : "Sure."