Snow depth (SD) estimations are very valuable in particular for snow-hydrological modelling, water resource management, ecological studies, and natural hazard assessment such as avalanche forecasting. In statistical SD models, snow-covered area is often used as a source of information. This study explores whether including additional snow cover geometrical descriptors, i.e., the second and third Minkowski functionals: total perimeter (MF2) and Euler-Poincaré characteristic (MF3), improves SD estimation. We performed two different SD simulation setups employing a Random Forest regression framework in the Tuolumne River Basin, California, U.S., at a 500 m resolution. We used the high-resolution remote sensing-derived SD maps of the multi-year Airborne Snow Observatory (ASO) dataset (2013–2016) at a 3 m spatial resolution for model development regarding the geometrical descriptors and evaluation regarding SD. In the baseline setup (BL-MF1), we trained the model with fractional snow-covered area, being the first Minkowski functional (MF1), topographic, and geographic variables. In the enhanced setup (EN-MF123), we also applied MF2 and MF3. Model performance, assessed by using R 2 , RMSE, MAE and MBE was compared between the enhanced model run including MF2 and MF3 and the baseline simulation. Results show that adding MF2 and MF3 ( R 2 = 0.87, RMSE = 0.17 cm, MAE = 0.10, MBE = 0.00) consistently improves model accuracy across diverse snow conditions and topographies compared to the baseline ( R 2 = 0.85, RMSE = 0.19 cm, MAE = 0.11, MBE = 0.00), however, with both variants performing in general well. The inclusion of the additional descriptors was beneficial in late-season melt conditions and fragmented snow cover areas, as the spatial structure captured by the geometrical descriptors improved prediction accuracy and reducing overestimation errors. However, the largest improvements were observed in deep, homogeneous snow cover areas where traditional predictors showed less variability. The methodology shows potential for enhancing snow-hydrological and avalanche risk models, with future work exploring its scalability across different mountain environments and spatial resolutions including different remote sensing products, and applicability to snow water equivalent estimation.