Solar absorption decays exponentially with depth in snowpacks. However, most climate models constrain all snowpack absorption to occur uniformly in the top-most snow layer. We show that 20--45% of solar absorption by deep snowpacks occurs more than 2 cm beneath the surface. Accounting for vertically-resolved solar heating alters steady-state snow mass without changing bulk snow albedo, and ice-albedo feedback amplifies this effect. Vertically-resolved snowpack heating reduces winter snow mass on the Tibetan Plateau by 80% in one GCM, and significantly increases 2 m air temperature. These changes significantly reduce model-measurement discrepancies. Our results demonstrate that snowpack radiative heating plays a significant role in regulating surface climate and hydrology. More accurate snowpack radiation has the potential to improve predictions of related climate processes, such as spring runoff and the Asian Monsoon.