The strong cold front and low pressure system will be at its most severe on Tuesday, the Bureau of Meteorology forecasts.
"Residents of southeast South Australia, Victoria, Tasmania and eastern New South Wales and parts of southern Queensland will be impacted by this system," the BOM says.
"Significant snow and rain with possible severe thunderstorms and hail is also expected ... mostly impacting western and central NSW, and western Victoria and Melbourne."
Snow levels are expected to rapidly drop on Tuesday to 600-700 metres across Victoria, Tasmania and southeast NSW, and above 800m in the NSW Central Tablelands.
Significant snow on alpine peaks of 20-50cm is likely with blizzard conditions.
The bureau warns the low-level snow and windy conditions will create particularly hazardous driving conditions, with inland highways likely to be hit by sleet.
Maximum temperatures are expected to be 3-6C below the May average, including in areas as far inland as southern Queensland and southern NT.
The cold front is also bringing large swells that will batter most of the southern Australian mainland, in particular South Australia and western Victoria.
Severe weather warnings for damaging wind gusts are in place for much of South Australia and NSW, plus northern Victoria.
"These areas have also recently seen significant rainfall meaning winds over sodden catchments may see fallen trees (and) powerlines and impacts to caravans and motorhomes," the BOM warns.
"There will likely be damage to property and weakened trees, with possible flash flooding due to blocked drains."
The damaging winds are likely to ease late on Wednesday.
8°C