One of the names of Succot is זמן שמחתינו, the time of joy. שמחה is a very powerful emotion and is a prerequisite towards achieving greater spiritual heights.
It is told that the Prophet, Yona Ben Amitai, of whale fame, felt the שכינה, Divine Presence, rest upon him when he participated in the festivities of the שמחת בית השואבה in the Beit Hamikdash.
The Rambam clearly wrote that in order to achieve prophecy, the prophet had to elevate himself with music, to raise his spirits. Once he was in a state of joy, he was able to communicate with Hashem.
In Chassidut, they speak of שמחה as a powerful tool in not only overcoming sadness, but even sickness. So we see that Succot is showing us how it really is a Mitzva to always be בשמחה.