Goulburn winters are always quite cold, dead winters sometimes hitting minus temperatures. Coldest winter temp I have had In goulburn is about -12C. There's always a chance of snow here and is sometimes for cast, but usually the snow misses goulburn and hits surrounding areas like Crookwell. I've lived in goulburn for about 3 years and it has snowed once for approximately 2 hours. But it was beautiful.
I used to live in Goulburn and my father will be moving back there shortly. Goulburn can get cold especially at night. I have attached the Weatherzone forecast for your reference.
It snows rarely - once a year at most and it doesn't last long.
Yes it does snow but rarely for me the last time it snowed was in June 2019 I am not to sure of exactly when. Goulburn can get very cold but also pretty hot it can get to lower than -5°