Where can i play with snow at australia?will be going there this 1st june?

i am going to melbourne this 1st of june 2010. and i wonder if it is already winter at that time?can anyone give me an idea where to go so dat i can play around with snow preferably near melbourne such as falls creek, mount hotham, butler?is it already snowy at that time?any place?as long as there's snow?tasmania?