Snowpack accumulation/ablation affects the runoff response to precipitation by modulating the water flux reaching the surface. Previous studies mostly focused on “rain‐on‐snow” events. Here we propose a framework to extend the scope and classify precipitation events accompanied by snow accumulation/ablation (precipitation‐and‐snow, or PAS, events) into five regimes. This framework is applied to a regional climate simulation over the western United States for 1981–2015 to reveal regions where daily changes in snowpack alter the surface hydrologic responses to precipitation. Over the western United States, PAS events account for 50–90% of all the precipitation events. Compared to the broad spatial distribution of snow accumulation‐type PAS events, snowmelting‐type PAS events are limited to coastal high‐elevation areas. Atmospheric rivers, a key driver of heavy precipitation in the region, account for only 2% of the PAS events, but they trigger significant snowmelt, accounting for 20% and 11% of light and heavy snowmelting events, respectively.