Despite being the main sediment entrainment mechanism in aeolian transport, granular splash is still poorly understood. We provide a deeper insight into the dynamics of sand and snow ejection with a stochastic model derived from the energy and momentum conservation laws. Our analysis highlights that the ejection regime of uniform sand is inherently different from that of heterogeneous sand. Moreover, we show that cohesive snow presents a mixed ejection regime, statistically controlled either by energy or momentum conservation depending on the impact velocity. The proposed formulation can provide a solid base for granular splash simulations in saltation models, leading to more reliable assessments of aeolian transport on Earth and Mars.