Mountainous basins are frequently called “natural water towers” because they supply essential water to downstream regions for irrigation, industrial–municipal use, and hydropower generation. The possible implications of climate change on water supplies have gained prominence in recent years, particularly in snow-dominated mountainous basins. The Euphrates River, a snow-fed transboundary river that originates from the Eastern part of Türkiye with several large dam reservoirs downstream, was chosen within this scope. The study reveals the impact of climate change on two snow-dominated headwaters, namely Karasu and Murat, which have a basin area of 41,109 km2. The impact of climate change is assessed across runoff regimes and snow dynamics for future periods (2024–2099). Global Climate Model (GCM) data sets (CNRM-CM5, IPSL-CM5A, EC-EARTH, MPI-ESM-LR, NorESM1-M, HadGEM2-ES) were downscaled by Regional Circulation Models (RCMs), provided from CMIP5 EURO-CORDEX domain for climate projections under RCP4.5 and RCP8.5 scenarios. Future projections of runoff and snow variables are predicted by two conceptual hydrological models, HBV and HEC-HMS. The results indicate a dramatic shrink in snow cover extents (>65%) and snow duration (25%), a decrease in snow water equivalent (>50%), and a timely shift (up to a month) in peak runoff through early spring in the runoff hydrograph for the last future period (2075–2099). The overall assessment shows that operations of downstream water systems should be reconsidered for future changes.