The increasing adoption of satellite Internet with low-Earth-orbit (LEO) satellites in mega-constellations allows ubiquitous connectivity to rural and remote areas. However, weather events have a significant impact on the performance and reliability of satellite Internet. Adverse weather events such as snow and rain can disturb the performance and operations of satellite Internet's essential ground terminal components, such as satellite antennas, significantly disrupting the space-ground link conditions between LEO satellites and ground stations. This challenge calls for not only region-based weather forecasts but also fine-grained detection capability on ground terminal components of fine-grained weather conditions. Such a capability can assist in fault diagnostics and mitigation for reliable satellite Internet, but its solutions are lacking, not to mention the effectiveness and generalization that are essential in real-world deployments. This paper discusses an efficient transfer learning (TL) method that can enable a ground component to locally detect representative weather-related conditions. The proposed method can detect snow, wet, and other conditions resulting from adverse and typical weather events and shows superior performance compared to the typical deep learning methods, such as YOLOv7, YOLOv9, Faster R-CNN, and R-YOLO. Our TL method also shows the advantage of being generalizable to various scenarios.