Under different climate change scenarios, the current study was planned to simulate runoff due to snowmelt in the Lidder River catchment in the Himalayan region. A basic degree-day model, the Snowmelt-Runoff Model (SRM), was utilized to assess the hydrological consequences of change in the climate. The performance of the SRM model during calibration and validation was assessed using volume difference (Dv) and coefficient of determination (R2). The Dv was found to be 11.7, −10.1, −11.8, 1.96, and 8.6 in 2009–2014, respectively, while the respective R2 was 0.96, 0.92, 0.95, 0.90, and 0.94. The Dv and R2 values indicate that the simulated snowmelt runoff closely agrees with the observed values. The simulated findings were assessed under three different climate change scenarios: (a) an increase in precipitation by +20%, (b) a temperature rise of +2 °C, and (c) a temperature rise of +2 °C with a 20% increase in snow cover. In scenario (b), the simulated results showed that runoff increased by 53% in summer (April–September). In contrast, the projected increased discharge for scenarios (a) and (c) was 37% and 67%, respectively. The SRM efficiently forecasts future water supplies due to snowmelt runoff in high elevation, data-scarce mountain environments.