The variations in snow cover on the Tibetan Plateau play a pivotal role in comprehending climate change patterns and governing hydrological processes within the region. This study leverages daily snow cover data and the NASA Digital Elevation Model (DEM) from 2003 to 2020 to analyze spatiotemporal snow cover days and assess their responsiveness to climatic shifts by integrating meteorological data. The results reveal significant spatial heterogeneity in snow cover across the Plateau, with a slight decreasing trend in annual average snow cover duration. Snow cover is predominantly observed during the spring and winter seasons, constituting approximately 32% of the total snow cover days annually. The onset and cessation of snow cover occur within a range of 120–220 days. Additionally, an increasing trend in snow cover duration below 5000 m altitude was observed, in addition to a decreasing trend above 5000 m altitude. Sub-basin analysis delineates the Tarim River Basin as exhibiting the lengthiest average annual snow cover duration of 83 days, while the Yellow River Basin records the shortest duration of 31 days. The decreasing trend in snow cover duration closely aligns with climate warming trends, characterized by a warming rate of 0.17 ± 0.54 °C per decade, coupled with a concurrent increase in precipitation at a rate of 3.09 ± 3.81 mm per year. Temperature exerts a more pronounced influence on annual snow cover duration variation compared to precipitation, as evidenced by a strong negative correlation (CC = −0.67). This study significantly augments the comprehension of hydrological cycle dynamics on the Tibetan Plateau, furnishing essential insights for informed decision-making in water resource management and ecological conservation efforts.