Interesting question, FreeMoney. Sunrise and sunset are measured from the penetration of the edge of the sun above and below the horizon, not the center of the sun, so day and night are not equal on the equator year round.
Also, according to my pen on napkin sketches, the sun rises slightly to the north south of the tropic of cancer when the northern hemisphere is in summer, and the sun rises slightly to the south north of the tropic of capricorn during northern winter.
So, my guess is that the equator is experiencing a summer solstice. In fact every where south of 23° N is experiencing
diurnal winter. This leads me to some tropical paradoxes however. Please attack my logic. I've run out of space on my napkin.
Rest assured, it is in fact winter in Greenland, with 3 meters of snow and no direct sunlight for the past nine days.
I'm not quite accustomed to the terminology, but using the term "summer solstice" at the equator is not very reasonable for the winter solstice of the northern hemisphere. That just assumes the northern view more important, and raises the question where to place the border between the two approaches.
The equator has a six-month cycle in terms of solar power, just the direction (North vs South) is different every half year. I don't see how defining "summer" and "winter" would have a lot of meaning to the people there. From what I can remember, many just assume northern hemisphere terminology though, since that's what the majority of tourists uses -- and those are the people who like thinking in "summer and winter" year cycles instead of rain periods etc.
PS: yay highjacking of threads.