We report on wind-tunnel measurements of particle velocity distribution in aeolian transport. By performing extended statistics, we show that for saltation occurring over an erodible bed the vertical lift-off velocity distributions deviate significantly from a Gaussian law and exhibit a long tail accurately described by a lognormal law. In contrast, saltation over a rigid bed produces Gaussian velocity distributions. These results strongly suggest that the deviation from Gaussian distributions is a consequence of the splash process which is exclusively present in saltation transport over an erodible bed. We further suggest that the non-Gaussian statistics is intimately related to the statistical properties of a single splash event which produces ejection of particles with lift-off velocities distributed according to a lognormal law. This lognormal behavior can be simply inferred from the propagation process of the impact energy through the granular bed which can be viewed as the analog of a fragmentation process. These findings emphasize the crucial role of the splash process in saltation transport.