Southern hemisphere seasons?

In English-speaking nations south of the equator, is the period from the December solstice to the March equinox named "winter" or "summer"? I know that it is warmer than in the northern hemisphere because of the tilt of the earth's axis. What I'm wondering about is the name. If the names are opposite (northern hemisphere's "winter" = southern hemisphere's "summer"), what do you call it if you live on the equator?