Snow cover plays an important role in biotic and abiotic environmental processes, as well as human activities, on both regional and global scales. Due to the difficulty of in situ data collection in vast and inaccessible areas, the use of optical satellite imagery represents a useful support for snow cover mapping. At present, several operational snow cover algorithms and products are available. Even though most of them offer an up-to-daily time scale, they do not provide sufficient spatial resolution for studies requiring high spatial detail. By contrast, the Let-It-Snow (LIS) algorithm can produce high-resolution snow cover maps, based on the use of both the normalized-difference snow index (NDSI) and a digital elevation model. The latter is introduced to define a threshold value on the altitude, below which the presence of snow is excluded. In this study, we revised the LIS algorithm by introducing a new parameter, based on a threshold in the shortwave infrared (SWIR) band, and by modifying the overall algorithm workflow, such that the cloud mask selection can be used as an input. The revised algorithm has been applied to a case study in Gran Paradiso National Park. Unlike previous studies, we also compared the performance of both the original and the modified algorithms in the presence of cloud cover, in order to evaluate their effectiveness in discriminating between snow and clouds. Ground data collected by meteorological stations equipped with both snow gauges and solarimeters were used for validation purposes. The changes introduced in the revised algorithm can improve upon the overall classification accuracy obtained by the original LIS algorithm (i.e., up to 89.17 from 80.88%). The producer’s and user’s accuracy values obtained by the modified algorithm (89.12 and 95.03%, respectively) were larger than those obtained by the original algorithm (76.68 and 93.67%, respectively), thus providing a more accurate snow cover map.