The declared ski season runs from the June long week end until the October long week end each year. Snow often falls well before the ski season starts. The snow is usually at its peak depth and condition in August but this does vary between seasons and it can often can be better in July. By September days start to get longer and “warmer” but there can still be awesome “spring skiing” and the rates are a lot cheaper.
The major resorts all now have extensive snow making facilities top keep the runs in great conditions regardless of snowfalls. You can ski from top to bottom at Thredbo more days per year now than you could in yesteryear even when there was huge snow seasons.