A trough will cross the southeast of the country on Sunday into Monday, while the associated cold front slides southwards. This system peaked over Western Australia, so the cold air does not reach the alps and neither does the precipitation.
The trailing high will stay centred just enough back to our west, so a cold front can move through on Tuesday into Wednesday. This one peaks here and should deliver around 5 cm snow on Tuesday night into Wednesday morning, falling down to around 1300 metres for a time. The following surge (trough) gets pushed southwards and the high moves in on Friday.
High pressure moves eastwards, letting it warm up again. There may be a trough over the weekend.
Commentary above courtesy of Jane's Weather. www.janesweather.com