In this study, a Bayesian framework is proposed for investigating uncertainties in input data (i.e., temperature and precipitation) and parameters in a distributed hydrological model as well as their effects on the runoff response in the Kaidu watershed (a snowmelt–precipitation-driven watershed). In the Bayesian framework, the Soil and Water Assessment Tool (SWAT) is used for providing the basic hydrologic protocols. The Delayed Rejection Adaptive Metropolis (DRAM) algorithm is employed for the inference of uncertainties in input data and model parameters with global and local adaptive strategies. The advanced Bayesian framework can help facilitate the exploration of variation of model parameters due to input data errors, as well as propagation from uncertainties in data and parameters to model outputs in both snow-melting and nonmelting periods. A series of calibration cases corresponding to data errors under different periods are examined. Results show that 1) input data errors can affect the distributions of model parameters as well as parameters’ correlation, implying that data errors could influence the related hydrologic processes as well as their relations; 2) considering input data errors could improve the hydrologic simulation ability for peak streamflows; 3) considering errors of temperature and precipitation data as well as uncertainties of model parameters can provide the best modeling simulation performance in the snow-melting period; and 4) accounting for uncertainties in precipitation data and model parameters can provide the best modeling performance during the nonmelting period. The findings will help enhance hydrological model’s capability for simulating/predicting water resources during different seasons for snowmelt–precipitation-driven watersheds.