Mountainous watersheds have always been a challenge for modelers due to large variability and insufficient ground observations, which cause forcing data, model structure, and parameter uncertainty. This study employed Differential Evolution Adaptive Metropolis (DREAM) algorithm which utilizes Markov Chain Monte Carlo (MCMC) approach to account for forcing data uncertainty. A conceptual degree day snowmelt model, MIKE 11 NAM (Nedbor Afstromnings Model), was used to simulate snowmelt runoff from Ilgaz basin, with an area of 28.4 km2 area, located in the northern part of Turkey. The mean elevation is around 1700 m and the basin is covered with broadleaf forest and has mainly brown soil with a high water holding capacity. Precipitation and evapotranspiration (ET) values were optimized in combination with model parameters conditioned on observed discharges and corrected values of input data were utilized for calibration and validation. Results showed that the observed precipitation was over-estimated by almost 10%, while evapotranspiration calculated by Penman–Monteith method was underestimated. The mean values of storm and ET multipliers were obtained as 1.14 and 0.84, respectively. When only parameter uncertainty was considered, calibration did not yield Nash Sutcliffe Efficiency (NSE) greater than 0.64. However, when forcing data uncertainty was incorporated in the DREAM approach, an improved value of NSE (0.84) was obtained. After calibration and treatment of forcing data errors, the model yielded reasonable prediction uncertainty bounds and well-defined posterior distributions of NAM model parameters. Main objectives of the study are to assess the applicability of MIKE 11 NAM model to the selected catchment. In addition, the importance of errors in the input forcing variables to the model is demonstrated.