With trends indicating increase in temperature and decrease in winter precipitation, a significant negative trend in snow-covered areas has been identified in the last decade in the Himalayas. This requires a quantitative analysis of the snow cover in the higher Himalayas. In this study, a nonlinear autoregressive exogenous model, an artificial neural network (ANN), was deployed to predict the snow cover in the Kaligandaki river basin for the next 30 years. Observed climatic data, and snow covered area was used to train and test the model that captures the gross features of snow under the current climate scenario. The range of the likely effects of climate change on seasonal snow was assessed in the Himalayas using downscaled temperature and precipitation change projection from -HadCM3, a global circulation model to project future climate scenario, under the A1B emission scenario, which describes a future world of very rapid economic growth with balance use between fossil and non-fossil energy sources. The results show that there is a reduction of 9% to 46% of snow cover in different elevation zones during the considered time period, i.e., 2011 to 2040. The 4700 m to 5200 m elevation zone is the most affected area and the area higher than 5200 m is the least affected. Overall, however, it is clear from the analysis that seasonal snow in the Kaligandaki basin is likely to be subject to substantial changes due to the impact of climate change.