There is a 50% chance of learning a new type of Snowman when building one. Traits determine the Snowmen you can make. Aside from Common, there are five other types:
Tragic Clown Snowman - Grumpy, Hates the Outdoors - also having a low mood (-40)
Hockey Snowman - Athletic, Loves the Outdoors - also having an ice skating rink on the lot.
Evil Snowman - Daredevil, Evil, Mean-Spirited, Hot-Headed, Pyromaniac (yes the hidden trait)
Reaper - Unlucky, Evil and having tombs/urns on the lot or in the inventory - part time job at mausoleum as well (harder to learn)
Alien - Insane, Computer Whiz (harder to learn)