A class of Martian impact craters with particularly unusual ejecta characteristics (double-layered ejecta (DLE) craters) are preferentially located in the midlatitudes in both hemispheres of Mars. Unlike today, decameters thick deposits of snow and ice occupied these same latitudes for significant periods during the Amazonian period. We assess the hypothesis that the unusual double-layer morphology could be related to impact into a snow and ice glacial substrate followed by landsliding of ejecta off of the structurally uplifted rim. We find that many characteristics of DLE craters (e.g., latitudinal distribution, lack of secondaries, landslide-like textures, evidence for overthrusting, relation to other crater types, etc.) are consistent with such an origin.