Due to data collection challenges, the mean-teacher learning paradigm has emerged as a critical approach for cross-domain object detection, especially in adverse weather conditions. Despite making significant progress, existing methods are still plagued by low-quality pseudo-labels in the degraded images. In this paper, we propose a generation-composition paradigm training framework that includes the tiny-object-friendly loss, i.e., IAoU loss with a joint-filtering and student-aware strategy to improve pseudo-labels generation quality and refine the filtering scheme. Specifically, in the generation phase of pseudo-labels, we observe that bounding box regression is essential for feature alignment and develop the IAoU loss to improve the accuracy of bounding box regression, further facilitating subsequent feature alignment. We also find that selecting bounding boxes based solely on classification confidence does not perform well in cross-domain noisy image scenes. Moreover, relying exclusively on predictions from the teacher model could cause the student model to collapse. Accordingly, in the composition phase, we introduce the mean-teacher model with a joint-filtering and student-aware strategy combining classification and regression thresholds from both the student and the teacher models. Our extensive experiments, conducted on synthetic and real-world adverse weather datasets, clearly demonstrate that the proposed method surpasses state-of-the-art benchmarks across all scenarios, particularly achieving a 12.4% improvement of mAP i.e., cityscapes to RTTS.