Glen Perrin said the conditions are likely to last until the early hours of Friday local time.
The national weather service said that more snow could fall above around 1000m in parts of Tasmania, including Mount Field and Mount Wellington.
A video shared on social media showed snow falling across a ski club in Ben Lomond, a mountain in the region’s north.
Mr Perrin from the Bureau of Meteorology said it was “not unusual for us to get snow at any time of year,” adding that the conditions were the result of cold air being blown in.
Blazes and flooding have plagued the country, with wet weather bringing relief from fires but causing its own set of problems.
Storms trigged flash flooding in parts of Australia in January, submerging areas of Brisbane and Queensland.
Authorities welcomed the promise of wet weather, which doused blazes as the country battled its worst wildfire season on record.
Fires have killed around one billion animals and at least 32 people since they started last year, as well as torching thousands of homes.
Emergency authorities in Victoria said on Thursday that there were no ongoing significant blazes, while New South Wales fire service – another region badly-hit by extreme weather – said firefighters were still working to battle “heightened level of activity” in some areas.