"zzz" denotes sleeping, and does not indicate snoring. Nobody knows the origin, but the use of "zzz" to denote sleep is only about 120 years old. It is not onomatopoeic - the "zzz" buzzing sounds is nothing like the sound of a snore.

It is used to show sleeping and sometimes snoring. It is not really a word, more of a sound and if you inhale through your nose, but really badly, as if you have a cold then that is something like it... Here is a link, but be warned it's very annoying! Hahaha!! https://www.youtube.com/watch?v=EnGiGeNYciM&t=5s

Sleeping...