The simple answer would be that we avoid any behavior that slaps the new yomtov of Shmini Atzeres in the face (such as shaking lulav). To eat in the sukkah is no big deal, as plenty of people eat on porches or gazebos or what-have-you when the weather's nice, no religious ritual required. So in places where it was ridiculously cold on Shmini Atzeres, they didn't!
There are Hassidic thinkers who have answers that give the practice more significance (often based on Hassidic or kabbalistic thought), but that would be the simplest answer.