No they're reversed. When I was little I used to think that it would be January in one hemisphere and June in the other.
I know the months are the same. When it's December in the North it's December in the South.
But when it's December in the North, we say the season is Winter.
I thought that when it's December in the South, they still call the season Winter, even though it's the warmest season, rather than calling it Summer.
But I guess I'm wrong.