Literally refers to young children, who often have colds but don't wipe their nose. Commonly used as a derogatory term to describe someone who is childish in behavior or appearance.
These snot-nosed kids tried to get into this club with their fake IDs, but the bouncer threw them out.
1) Employee: "I am so fresh out of school, that I practically don't know very much."
Boss: "So your just a regular snot nosed kid."
OR
2) "You don't even knowwhat you are talking about! Your probably nothing but some rambling snot nosed kid and need to seriously grow up!"
OR
3) "I can't imagine having any children. I mean who wants to deal with a pair of snot nosed little brats running around the house after a long day at work!"