The big question this week is: is there enough cold air?
An East Coast Low (ECL) is bringing huge rain, big winds and coastal effects to NSW from Monday to Thursday this week. It forms thanks to moist air meeting up with instability - and this instability comes from an upper level cold pool.
This cold pool arrived yesterday over the alps, and it's a decently cold pool of air that is bringing pockets of light snow on Monday. The cold pool is projected to remain in the area (driving the ECL) on Tuesday, weaken a little on Wednesday and disappear on Thursday.
Meanwhile, the ECL develops off northern NSW later on Monday, and slowly moves southwards, then out to sea over the next few days.
The huge rainfalls will be on the NSW coast, but some of this precipitation will reach the alps.
It'll come in from a southeasterly direction thanks to the location of the low.
Most likely, we'll see snow above around 1500 metres on Tuesday, 1600-1700 metres on Wednesday, and above 1800 metres on Thursday (as the falls ease). In western areas the snow may remain lower as it is closer to the cold pool.

Some areas may see as much as 40 or 50 cm of snow - if they pick up a good stream of precipitation. This also falls as rain lower down, and as the week progresses, the snow falling will become very wet snow, if it remains slightly frozen.
This is a tricky one, as you are combining a very tropical system with a punch of cold air - and it may not meet up properly at all times.
FURTHER AHEAD
Looking further ahead and we'll have two generally dry days on Friday and Saturday.
A weak system looks to move through on Sunday and Monday. Weak in terms of how much precipitation it brings, and weak in terms of how much cold air. It is borderline for the higher peaks, and only light falls.
Then there is something much better brewing - but it is currently due later Tuesday with the goods next Wednesday - way too far out for any confidence at this stage but watch this space!