The main East Coast Low centre (ECL) that brought severe weather to southeast NSW and VIC is on its way out to sea late Monday morning. This means the rain will rapidly ease this afternoon.
A new low centre (currently south of Adelaide) will join up with the remains of the ECL, and we will end up with a low centre just east of Tasmania for Tuesday. This positioning, and a weak pool of cold air, will sling-shot precipitation around it and up into the alps. I'd expect snow above around 1700 metres this afternoon and tonight, lowering to 1500 metres for the coldest part Tuesday morning and early afternoon, then rapidly turning back to rain as it moves away later on Tuesday (also easing the precipitation). This could deliver 10cm up high, before a little wash away at the end (Tuesday night/Wednesday morning).
Then there is more to come...
The cold front approaching Perth will join up with the low off northwest WA, forming another cut-off low. This system has plenty of tropical moisture (have a look at the satellite) and plenty of cold air in behind it - but both of these things will significantly reduce by the time it affects the alps.
The low moves to our south late Wednesday/early Thursday, and a trailing trough moves through later Thursday. Precipitation redevelops Wednesday night and lasts through to early Friday, heaviest on Thursday morning. But its only cold enough for a wet snow mix above ~1700 metres, that could bring 20 to 30 cm up high if we are lucky.
The long weekend kicks off with a bang - a proper cold front on Saturday. This one has no warm air at all, but no tropical moisture feed, so its a moderate fall of good-quality snow, down to 1000 metres for a time. Expect 10 to 15 cm from this one.
My snow forecasts start at www.janebunn.net on June 10th.