Water storage (WS) is a crucial terrestrial ecosystems service function. In cold alpine regions (CAR), the cryosphere elements are important solid water resources, but the existing methods for quantitatively assessing WS usually ignore cryosphere elements. In this study, a revised Seasonal Water Yield model (SWY) in the Integrated Valuation of Ecosystem Services and Trade-offs (InVEST), which considers the effects of frozen ground (FG) and snow cover (SC) on WS, was employed to estimate the spatiotemporal distribution and changes in WS in the Three-Rivers Headwaters region (TRHR) from 1981 to 2020. Sensitivity analyses were conducted to understand the overall effects of multiple factors on WS, as well as the dominant driving factors of WS change at the grid scale in the TRHR. The results show that (1) the WS in the TRHR generally increased from 1981 to 2020 (0.56 mm/year), but the spatial distribution of WS change varied greatly, with a significant increasing trend in the northwest part and a significant decreasing trend in the southeast part. (2) In the last 40 years, increased precipitation (Pre) positively affected WS, while increased potential evapotranspiration (ET0) reduced it. Increased permeability caused by degradation of frozen ground increased WS, while snow cover and LULC changes reduced it. (3) In the TRHR, Pre primarily affected the WS with the largest area ratio (32.62%), followed by land use/land cover (LULC) (19.69%) and ET0 (18.49%), with FG being fourth (17.05%) and SC being the least (6.64%). (4) The highly important and extremely important zones generally showed a decreasing trend in WS and should be treated as key and priority conservation regions. It is expected that this research could provide a scientific reference for water management in the TRHR.