August is the end of winter, though spring can see more snow than winter. "downhill" skiing with ski-lifts operate at Mt Field near Hobart in the south
and Ben Lomond nearrLaunceston in the north
There is extensive areas under snow for cross country skiiing but the terrain is difficult and walking tracks such as the Overland Track are skied only by those with a good deal of experience.
http://en.wikipedia.org/wiki/Overland_Track about 6 years ago
agreed, ben lomond tends to have a later season than the mainland and does have a few nice cross country tracks, you'll possibly need chains to get up there if you score some snow (the parks dudes stopped us for not carrying them, but that was reasonably early in the season). enjoy about 6 years ago