The standard freeze-in paradigm has a hidden UV sensitivity in that the initial DM population is assumed to be exactly zero. We explore how a pre-existing population of DM, either alone or as part of a thermalized dark sector, affects the dynamics of freeze-in. The UV sensitivity of this more general scenario, which we dub “glaciation”, is manifested in the dependence of the late-time relic abundance on the size of the initial population. We dispense rather quickly with the case of a stand-alone initial DM abundance, which simply leads to an offset in the relic abundance compared to the standard scenario, but we find rich and interesting dynamics in the case of a pre-existing thermalized dark sector. Our results have important consequences for direct detection experiments searching for freeze-in dark matter.