Accurate simulation of snow cover process is of great significance to the study of climate change and the water cycle. In our study, the China Meteorological Forcing Dataset (CMFD) and ERA-Interim were used as driving data to simulate the dynamic changes in snow depth and snow water equivalent (SWE) in the Irtysh River Basin from 2000 to 2018 using the Noah-MP land surface model, and the simulation results were compared with the gridded dataset of snow depth at Chinese meteorological stations (GDSD), the long-term series of daily snow depth dataset in China (LSD), and China’s daily snow depth and snow water equivalent products (CSS). Before the simulation, we compared the combinations of four parameterizations schemes of Noah-MP model at the Kuwei site. The results show that the rainfall and snowfall (SNF) scheme mainly affects the snow accumulation process, while the surface layer drag coefficient (SFC), snow/soil temperature time (STC), and snow surface albedo (ALB) schemes mainly affect the melting process. The effect of STC on the simulation results was much higher than the other three schemes; when STC uses a fully implicit scheme, the error of simulated snow depth and snow water equivalent is much greater than that of a semi-implicit scheme. At the basin scale, the accuracy of snow depth modeled by using CMFD and ERA-Interim is higher than LSD and CSS snow depth based on microwave remote sensing. In years with high snow cover, LSD and CSS snow depth data are seriously underestimated. According to the results of model simulation, it is concluded that the snow depth and snow water equivalent in the north of the basin are higher than those in the south. The average snow depth, snow water equivalent, snow days, and the start time of snow accumulation (STSA) in the basin did not change significantly during the study period, but the end time of snow melting was significantly advanced.