Surface ice at the poles of Mercury appears as several-m-thick deposits that are composed of nearly pure water. We provide new age estimates of Mercury's polar deposits from combined analyses of Poisson statistics and direct observations of crater densities within permanently shadowed, radar-bright regions imaged by the MESSENGER spacecraft. These age estimates suggest that ice was delivered to Mercury within the last ~150 Myr. A single, recent impactor is one possible delivery mechanism that is consistent with our new age constraints, as well as the observed distinct reflectance boundaries of the polar deposits and the relative purity of the ice, as suggested by the Earth-based radar observations. In contrast to ice on Mercury, observations of the lunar poles are suggestive of a highly patchy distribution of surface frost. The patchiness of lunar polar deposits is consistent with long exposure times to the space weathering environment. Given enough time, the polar deposits on Mercury may age into a more heterogeneous spatial distribution, similar to that on the Moon.