In January, is it winter in Australia?

I mean, everyone knows that in January it's hot in Australia, and in July it's cold there.

But do Australians call it "winter" in January and "summer" in July? Or does just "winter" imply hot weather and beaches, and "summer" implies winter, eh, i mean, snow sports and wool socks.

And given that, most of the population lives in northern hemisphere, is there a body of dad jokes and culture tropes related to the fact that "we're different", or is it just too cringe and boring. (I realize both could be true on this one.)