No one ever said Winters in Oz aren't cold, although it's a big place so how cold depends on where you are. The difference is that Winters here are short, (6 - 10 weeks, depending on where you live) and Summer is the dominate season with hot weather sometimes starting as early as August and going through to March or later.
You will definitely need jumpers, coats etc for most of the southeast even if you only wear them for a few weeks.
A lot of homes in the cooler regions have ducted heating or reverse cycle air conditioning with the air con getting much more use.
For the last 7 years much of the continent has been suffering from severe drought with higher than normal temps so a return to more normal, cooler weather with rain, which we've had in the southeast this season, has been more then welcome. Sydney's dams are currently at 57% capacity and we're on stage 3 water restrictions, see
Mandatory Water Restrictions Brisbane is on stage 5. I think all the major centres except perhaps Darwin have water restrictions of some kind.