The valley of Kashmir being an extremely ecologically sensitive area deserves significant attention with regard to climate change. As the region is part of the Indian Himalayan Region (IHR) and home to multiple rivers and glaciers, it holds significant geopolitical, economic, as well as geographical importance. Climate change in the region can have ripple effects on the Indian subcontinent in general. As such effective prediction of the different climate variables of the region is of paramount importance and can help us to reverse or slow down the negative climate change process. In this paper, we investigate CRU TS4.04 time series data of 120 years (1901-2019) for three major climate variables - precipitation, temperature, and cloud cover observed in the region. The analysis revealed some key and concerning trends. Thereafter, forecasting of the climate parameters for the next 80 years (2020-2100) was performed using the ARIMA and S-ARIMA models after a thorough analysis of the data and proper hard tuning of the model hyper-parameters, separately for each of the three climate parameters. The resulting projections show drastic temperature changes, with a projected increase of about 2°C by the end of the century, slight changes in precipitation and cloud cover, and other alarming climatic conditions. This study also brings forth the inability of the ARIMA model to substantially forecast erratic changes in any climate variable. The insights gathered in this study may serve as a presage for the concerned government and stakeholders, and will pave way for the development of robust and efficient plans to tackle climate change in the area. This is the first kind of work that is using effective machine learning-based time-series forecasting models trained over such a large data set for all three major climate variables.