A workmate just pointed me to this: http://www.snow-forecast.com/maps/dynamic/tasmania
It appears to be a very useful tool, although I'll reserver my judgement as to how accurate it is after this weekend when it is forecasting snow to various part of the central plateau for the next three days, but mostly on Sunday.
After the page loads, don't change any of the settings (if it's the snow forecast you're interested in). Just leave it set to 'Snow Forecast', and ignore the overlay section.
All you need to do is drag the slider along to see the forecast for each 12 hour period for the next few days.