I just got home from Pagan Spirit Gathering. Lots of talk of Solstice, no one claiming it was the first day of summer. Joyousness! I *am *glowing. It’s the glow of righteousness. Or perhaps sunburn. Ow. 
It’s true that what we call the first day of summer is just a matter of tradition and convention. At the same time, though, most people have the idea that summer is the warmest season. This year the vernal equinox happened on March 20, and the summer solstice on June 21. The halfway point between these two is May 5 or 6. Does anyone really think spring ends and summer begins in early May?
Just a little, we had the winter solstice on June 21 no problems. For us, we consider June 1 to be the first day of Winter though.
Edit, just saw Guanolad got in before me. And I agree, it’s frigging freezing atm.