It seems likely that Bushy Park ( near sealevel ) in Tasmania's Derwent Valley ( 65km/40miles inland from Hobart ) has recorded a sub zero maximum temperature in the past. This district is suspectible to day long fogs in the wintertime, following very low overnight temperatures, as cold air drains into the valley from the central plateau highlands.
The complete weather record for Bushy Park ( dating back to the 1870s I believe ) is not availble on the weather bureau's website, but on June 19 1992 a maximum of 0.0 is listed, following an overnight low of -4.9.
In Hobart on the 19th, it was 6.0 degrees maximum ( 6 below average ), and the capitals topography doesn't allow fogs to persist usually after mid morning - so - I am trusting that Bushy Park figure is reliable!
Red = Hobart Blue=Bushy Park
Derwent Valley Tasmania