Chanukah occurs when it does in order that we are lighting candles at the
time of maximum darkness--the new moon closest to the winter solstice:
if Hanukkah is not merely a solstice but a darkness festival, then the 25th of Kislev is the perfect time. In some years, the solstice day itself would be a night of bright full moon--especially powerful in an agrarian-pastoral culture with few artificial lights. So even the solstice itself would feel less like the darkest day of the year on such a moonlit night. By setting Hanukkah on the 25th of the month, the Jews made sure that the night would be dark. By setting it in Kislev, they made sure the day would be very short and the sun very dim. [Rabbi Arthur Waskow at My Jewish Learning]
In that case, Jews in the southern hemisphere really should celebrate the holiday in Sivan or Tamuz, no? And adopt a
summer-solstice festival in Kislev.