The two times i have climbed Snowy, i made both trips over-nighters. Thier are 2 camp sites (non offical) ABOUT 1/2 mile from the teail head.
Also camping on the summit is fun. it is the 8th highest mountain you can camp on and on clear mnorings and day's it has views to the High Peaks.
Pleas if you camp on top and make a fire do it on the big rocks at the clearing by the summit. (look at my picture of the tent on the ledge, those rocks) and make a fire ring. put drit on the bottom of it and when you are done put the rocks back and disperse the dirt. You know, "Light is Right" and all.