Do we know why this happened? In a world context, beginning the year in spring is normal; beginning it in the middle of winter is very weird indeed.
And it's not like this was a restoration of an older tradition. Four of the months are still literally named on the assumption that the first month of the year is March.
Right. Also, with March being the first month of the year, the variable-length month becomes the last one. On leap years, you add a day at the end of the year. Which is reasonable, unlike the current situation.
They had a perfectly sane calendar system and somebody just had to break it.
The character of the seasons is rather local. For example take the Greek legend of Persephone and Demeter and the Sumerian legend of Dumuzid and Inanna. Both explain the seasons by a god being trapped in the underworld for half the year, but the Greeks considered winter the dead time while for the Sumerians it was summer.
This is most definitely false; tracking the solstices with pinpoint accuracy was a goal of ancient cultures since before the beginning of recorded history.