Our northern winter is in Dec, Jan and Feb, whereas the southern winter is in June, July, and August. Each of our summers is 6 months away from our winters in our respective hemispheres. In cold places in either hemisphere (which thankfully doesn't include Hawaii) people might say: "I'll be glad when summer gets here and the weather warms up". The difference is that in the North people might say "I am dreading a cold January" whereas in the South you might say "I am looking forward to a warm January".
In short, False.