It’s a complete misconception that the seasons have anything to do with the signs. Erase that misconception.
There is the equator and the ecliptic. The ecliptic is the path of the Sun, and the equator is the center of the Earth. The equator is the “horizon” of space. The Sun spends half of the year above it and the other half below it. When it crosses the equator coming upwards that represents “sunrise” on a cosmic-yearly scale (and is therefore the “beginning” of the zodiac). When it crosses the equator coming downwards, that represents “sunset.”
The elements and modes which give meaning to the signs do so with reference to their relation to these celestial (not northern or southern hemisphere specific) directions: celestial East, West, North and South. You can find out about this in detail if you download this class: Understanding the 12 Signs
The main portion of the character of the signs comes from their planetary ruler, anyway, not the elements and modes. And this is determined by speed / distance from the Sun – again nothing to do with anything northern or southern hemisphere specific.
I hope this clarifies