Hi Jimmy,
As a generic answer to your question, the dryer and colder air masses will create the best quality powder snow, but we would need 4000m mountain ranges like the USA to take true advantage of this. If our Snowy's are to get any reasonable snow, the DP is up around 4C on the SW coast of Victoria in a blistering SW wind. By the time that air mass climbs the Snowy's, it's dumped rain on the coast, plains and lower slopes. The DP is -4 to -6 and temperature is the same (since the air is saturated) as it tops the main range. This orographic wave extends well beyond 500mb and provided the air mass has enough moisture to a great height, this is the territory of 40-60cm overnight dumps. When all this clears, the overnight conditions are always dry and cold. Change the originating air mass to one that comes from the E-SE and the DP is around 8. Consequently, there's a greater risk of rain and wet snow. Move it to the NE at a 12C DP and our snow is history.
Without referring directly to my detailed analysis to support my analysis, these conclusions are based on the position of the SOI in May preceding the season described:
Strong La Niña: Lots of snow and rain. In colder 1970's years, more snow. In latter 1990's years, more rain. Dominated by E-NE winds @ 8-10C DP at 1000mb means -2 to 0C at 800mb early in the season caused by a late N-NE monsoon, these subtropical origin air masses hit the Snowy's as mostly wet snow and rain. These are also years of mid NSW and QLD dumps resulting from cutoff low pressure regions. The Snowy's gets onshore E-NE winds as a result of this also.
Medium La Niña: Tends to more snow than rain with more W-NW than E-NE. Some spectacular wet snow dumps ahead of cold fronts can result from moisture-laden NW winds. Sometimes initial Medium La Niña conditions swing to Light El Niño by mid to late August improving the snow year to late season cross country skiing pleasure (1992, 96).
Light La Niña: Winters are becoming dominated by where the Polar Wave sits with a few moist NW and NE interludes. Lots of variable snow years, particularly with SE winds resulting in light wind dumps rather than the usual howling blizzards.
Neutral: Similar to Light La Niña. Some of the best years come from Neutral conditions.
Light El Niño: Notable years of this nature (1964, 68, 81) mostly exhibit an optimal polar wave with the most spectacular seasons resulting from snowy NW winds before and low DP SW winds after frequent cold fronts. Big snow drifts result from constant wind with little respite throughout the season.
Medium El Niño: Seasons are becoming dominated by dryer cold front preceding conditions with less rain. This factor otherwise may save a bad season since the air masses following are also a bit dryer resulting in light-dry snow fall. The polar wave can often favour NZ under these conditions and when this happens most of the snow falls from S-SE orographic air flow off the Southern Tasman Sea. 2006 is one clear example of this feature, but the precipitation distribution was more typical of a Strong El Niño.
Strong El Niño: These are most often dry years with an early snowfall followed by almost nothing but the odd SE outbreak. The Polar Wave favours NZ. 1982 is one clear example followed by 2006 being a surprise candidate despite it's slightly negative SOI.
Now there are some notable exceptions which I could point out from a more detailed analysis. These occur when SSTs SW and S of the continent dominate the position of the polar wave right over the SE of Australia.
Snow is not so much a direct influence of El Niño but rather one of where the air mass originates and what topography and land types it travels over before it hits the Snowy's from given direction. Yes, El Niño influences this and also does the geography of the regions in the path of incident air masses. As I've outlined above, there are some typical La Niña and El Niño trends to note but this is no guarantee for the stated snowy outcome. As the planet warms up, the likelyhood of air masses hitting the Snowy's from the optimal direction with the optimal moisture content, height and DP will unfortunately diminish but there will still be some spectacular dumps, just like XMAS and Boxing day on Mt Baw Baw.