Despite the _______ weather, the outdoor event was a huge success.

The word "despite" indicates that the weather was challenging but did not prevent the success of the event. Therefore, the word that best fits the context of bad or challenging weather is "inclement" (severe, rough, or harsh; stormy.). (1) pleasant: If the weather was pleasant, it would typically contribute to the success of the event rather than being a factor that contrasts with it. (2) mild: Mild weather would not present a significant challenge and is generally favorable for outdoor events. (4) favorable: Favorable weather would be supportive of the event, not something that would make the event's success surprising.