OK many years of snowboarding coming in handy finally.
In Victoria snow chains Must be carries. 4wd/awd are exempt from fitting chains unless specifically designated. It has happened to me once that I needed to fit them.
Snow tyres make no difference to the regs here.
In NSW again snow chains must be carried and fitted where designated.
Unless you are in a 4wd/awd. Although I think they are in the process of changing that to a 4wd with LOW range will be exempt.
I have driven in snow/ice many times a year both with snow tyres and with out. In a vehicle without low range I would stick with chains.
However with low range such as a patrol or cruiser, in really bad conditions low range, mud tyres and dropped pressures have been all I needed.
Cheers
Evo