Glaciers in the Himalaya-Karakoram (HK) are critical for ensuring water-security of a large fraction of world's population that is vulnerable to climate impacts. However, the sensitivity of HK glaciers to changes in meteorological forcing remains largely unknown. We analyzed modelled interannual variability of mass balance (MB) that is validated against available observations, to quantify the sensitivity of MB to meteorological factors over the HK. Within the model, snowfall variability (0.06 m/yr) explains ~60% of the MB variability (0.28 m/yr), implying a sensitivity of MB on snowfall to the tune of several hundreds of percent. This stunningly high sensitivity of MB to snowfall offers crucial insights into the mechanism of the recent divergent glacier response over the HK. Our findings underscore the need for sustained measurements and model representations of the spatiotemporal variability of snowfall, one of the least-studied factors over the glacierized HK, for capturing the large-scale and yet region-specific glacier changes taking place over the HK.