Reliable snow cover mapping in mountainous regions is critical for hydrology, climate monitoring, and hazard risk management. This study presents the initial evaluation of the EUMETSAT H SAF H43 snow cover extent product—the first derived from the Flexible Combined Imager (FCI) aboard Meteosat Third Generation (MTG)—over the European Alps. The assessment was performed by comparing H43 with its predecessor H34, using daily MODIS MOD10A1 NDSI-based binary snow maps as the reference for the 2024–2025 winter season. Evaluation metrics, including Probability of Detection (POD), False Alarm Ratio (FAR), and Overall Accuracy (ACC), were calculated based on pixel-level agreement across December to February. To investigate terrain-dependent classification performance, the spatial distribution of false alarms (B) and missed detections (C) was analyzed across elevation zones and terrain aspect classes derived from the MODIS 1 km MODDEM product. Wind rose visualizations revealed that both products exhibit classification uncertainty in mid-elevation ranges (1000–2000 m), with H34 showing higher miss rates and H43 slightly more false alarms. In higher elevation bands (≥2000 m), H43 demonstrated improved stability across slope orientations and generally lower error rates. These findings highlight the enhanced snow retrieval capability of the H43 product in complex alpine environments and support its application in near-real-time snow monitoring.