Semantic segmentation under adverse conditions is crucial for ensuring robust and accurate visual perception in challenging weather conditions. The distinct characteristics of extreme scenarios hinder traditional segmentation paradigms, highlighting the necessity for tailored approaches for adverse weathers. Due to the scarcity of labeled data in such scenarios, the unsupervised domain adaptation paradigm is commonly utilized to leverage knowledge from normal weather conditions. Although existing methods strive to absorb information from labeled normal weather data and unlabeled adverse condition images, they face significant challenges due to weather unawareness and severe feature heterogeneity, thus struggling to effectively parse scenes under adverse conditions. In this paper, we propose a novel weather-aware aggregation and adaptation network that leverages characteristic knowledge to achieve weather homogenization and enhance scene perception. Specifically, we introduce amplitude prompt aggregation to capture essential characteristics from the Fourier frequency domain that are indicative of different weather conditions. Additionally, we employ weather heterogeneity adaptation to mitigate the inter-domain heterogeneity, thereby achieving feature homogenization across diverse environments. Extensive experimental results on multiple challenging benchmarks demonstrate that our method achieves consistent improvements for semantic segmentation under adverse conditions.