Falling in the Fall
D. Rubinstein wrote:
Why does Succot fall on the calendar after Yom Kippur, and not after Passover? Succot deals with the fact that we sat in huts in the wilderness after we left Egypt, and the clouds that protected us. We were sitting in those huts and had those clouds right when we left Egypt, so historically, Succot should come right after, or during, Pesach.
Dear D. Rubinstein
Passover is in the spring when the weather stars getting warmer; if we were to make huts in the spring, it might seem like we were just building vacation bungalows to escape from the heat. Therefore, the Torah commanded us to build our succah-booths in the fall when it starts getting cool, making it clear that the succah is a commandment and not a cabana.
The Vilna Gaon offers another explanation: The succah represents the clouds of glory with which G-d protected us in the desert. Hashem took away these clouds when we made the Golden Calf, and when He forgave us that year on Yom Kippur, the clouds came back. So, Succot celebrates the return of those clouds after the first Yom Kippur in the desert.