Glaciers’ mass balance and melting patterns can be monitored through the study of their facies. Whilst using Synthetic aperture radar (SAR) remote sensing data facilitates glaciology observations as it can be used under all weather conditions, the systemic backscatter intensity decay due to incidence angle (IA) variation makes classification even more challenging on such complex terrain. We investigate the classification accuracy of glacier facies using SAR data through a supervised learning algorithm that incorporates class-dependent local incidence angle correction. Focusing on the Holtedahlfonna and Kongsvegen glacier complexes in northeast Svalbard, we pre-process SAR data from Sentinel-1 using the SNAP toolbox. We then compare three Bayesian classifiers: one without any IA correction, one with a common IA slope correction, and the third incorporating a class-dependent IA slope correction. Our results show that per-class IA slope correction on training regions improves the models by around 30% compared to the naive one and around 10% from the common IA slope correction. When tested on the glaciers, their firn line could be mapped from 2017 to 2023 and a general retreat of 400-500 m is observed, changing to 3-4 km in some regions of Holtedalhfonna. However, when looking at regions of lower altitudes, regions with crevasses are largely misclassified. To aid crevasse classification, we finish this study by providing some insights on potential texture features, using either standard deviation or spatial Fourier transforms. In all, this work explores the extent to which class-dependent IA corrections should be included in SAR data analysis, contributing to enhanced glacier monitoring and climate research.