Real-world object detection is a challenging task where the captured images/videos often suffer from complex degradations due to various adverse weather conditions such as rain, fog, snow, low-light, etc. Despite extensive prior efforts, most existing methods are designed for one specific type of adverse weather with constraints of poor generalization, under-utilization of visual features while handling various image degradations. Leveraging a theoretical analysis on how critical visual details are lost in adverse-weather images, we design UniDet-D, a unified framework that tackles the challenge of object detection under various adverse weather conditions, and achieves object detection and image restoration within a single network. Specifically, the proposed UniDet-D incorporates a dynamic spectral attention mechanism that adaptively emphasizes informative spectral components while suppressing irrelevant ones, enabling more robust and discriminative feature representation across various degradation types. Extensive experiments show that UniDet-D achieves superior detection accuracy across different types of adverse-weather degradation. Furthermore, UniDet-D demonstrates superior generalization towards unseen adverse weather conditions such as sandstorms and rain-fog mixtures, highlighting its great potential for real-world deployment.