This study assesses snow response in the Assiniboine-Red River basin, located in the Lake Winnipeg watershed, due to anthropogenic climate change. We use a process-based distributed snow model driven by an ensemble of eight statistically downscaled global climate models (GCMs) to project future changes under policy-relevant global mean temperature (GMT) increases of 1.0 °C to 3.0 °C above the pre-industrial period. Results indicate that basin scale seasonal warmings generally exceed the GMT increases, with greater warming in winter months. The majority of GCMs project wetter winters and springs, and drier summers, while autumn could become either drier or wetter. An analysis of snow water equivalent (SWE) responses under GMT changes reveal higher correlations of snow cover duration (SCD), snowmelt rate, maximum SWE (SWEmax) and timing of SWEmax with winter and spring temperatures compared to precipitation, implying that these variables are predominantly temperature controlled. Consequently, under the GMT increases from 1.0 °C to 3.0 °C, the basin will experience successively shorter SCD, slower snowmelt, smaller monthly SWE and SWEmax, earlier SWEmax, and a transition from snow-dominated to rain-snow hybrid regime. Further, while the winter precipitation increases for some GCMs compensate the temperature-driven changes in SWE, the increases for most GCMs occur as rainfall, thus limiting the positive contribution to snow storage. Overall, this study provides a detailed diagnosis of the snow regime changes under the policy-relevant GMT changes, and a basis for further investigations on water quantity and quality changes.