Accurate information on snow cover extent plays a crucial role in understanding regional and global climate change, as well as the water cycle, and supports the sustainable development of socioeconomic systems. Remote sensing technology is a vital tool for monitoring snow cover’ extent, but accurate identification of shallow snow cover on the Tibetan Plateau has remained challenging. Focusing on the Three-Rivers Headwater Region (THR), this study addressed this issue by developing a snow cover discrimination model (SCDM) using a random forests (RF) algorithm. Using daily observed snow depth (SD) data from 15 stations in the THR during the period 2001–2013, a comprehensive analysis was conducted, considering various factors influencing regional snow cover distribution, such as land surface reflectance, land surface temperature (LST), Normalized Difference Snow Index (NDSI), Normalized Difference Vegetation Index (NDVI), and Normalized Difference Forest Snow Index (NDFSI). The key results were as follows: (1) Optimal model performance was achieved with the parameters Ntree, Mtry, and ratio set to 1000, 2, and 19, respectively. The SCDM outperformed other snow cover products in both pixel-scale and local spatial-scale discrimination. (2) Spectral information of snow cover proved to be the most influential auxiliary variable in discrimination, and the combined inclusion of NDVI and LST improved model performance. (3) The SCDM achieved accuracy of 99.04% for thick snow cover (SD > 4 cm) and 98.54% for shallow snow cover (SD ≤ 4 cm), significantly (p < 0.01) surpassing the traditional dynamic threshold method. This study can offer valuable reference for monitoring snow cover dynamics in regions with limited data availability.