Adverse weather conditions, such as rain, snow, and fog, severely degrade LiDAR semantic segmentation by introducing refraction, scattering, and point dropouts that compromise geometric integrity. While prior approaches ranging from weather simulation and mixing-based augmentation to domain randomization and regularization enhance robustness, they frequently overlook structural vulnerabilities inherent to object boundaries, corners, and highly sparse regions. To address this limitation, we propose a Light Geometry-Aware Adapter. This module aligns azimuths and applies horizontal circular padding to preserve neighbor continuity across the 0 deg-360 deg wrap-around boundary. Using a local-window K-Nearest Neighbors (KNN) search, it aggregates nearby points and computes lightweight local statistics, compressing them into compact geometry-aware cues. During training, these cues facilitate region-aware regularization, which effectively stabilizes predictions in structurally fragile areas. The proposed adapter is designed to be plug-and-play, complements existing augmentation techniques, and operates exclusively during training, incurring negligible inference overhead. Operating under a rigorous source-only cross-weather paradigm wherein models are trained on SemanticKITTI and evaluated on SemanticSTF without target-domain labels or fine-tuning, our adapter achieves a +3.4 mIoU improvement over strong data-centric augmentation baselines. Furthermore, it demonstrates performance comparable to advanced class-centric regularization methods. These findings highlight that geometry-driven regularization constitutes a critical pathway toward achieving highly robust, all-weather LiDAR segmentation.