I wonder what determines it.

I can remember first thinking about it (around the same age i figured out how to move my eyes) as a ribbon of days going around in a spiral. Eventually it settled into the ellipse/rectangle thing i described.

I often felt that the summer is something you climb up to (end of school, exam season in university, etc), and then after some smooth relaxed sailing you drop down towards the winter again (no more free time, got to do school and so on).

However, i can't quite say if that determined the orientation, or the metaphor came from the orientation.

So weird. Mine is a circle. I too have summer on top, but spring is on the left and fall on the right, so it goes clockwise.

And it's kinda tilted in the third dimension depending on which date it is.

Yeah, same. Summer months form the bottom edge of the square, and winter months the top.