Gday Medion
My advice is to head to Adaminaby, there is heaps of cheap accommodation around the area.
You can then head up the Snowy highway to Kiandra and Mt Selwyn. There is usually some snow around this area and best part is you will not need a parks pass to get to it if it has snowed down low enough.
You can toboggin at Mt Selwyn or anywhere on the road leading up to the area, just watch out for the hidden creeks etc.
This is where we usually head when we go up the snow, but we only live an hour or so away.
Cheers