¹⁰Be dating of moraines has greatly improved our ability to constrain the timing of past glaciations and thus past cold events. However, the spread in ages from a single moraine is often greater than would be expected from measurement uncertainty, making paleoclimatic interpretations equivocal. Here we present 28 new ¹⁰Be ages from ice‐cored Neoglacial moraines on Baffin Island, Arctic Canada, and explore the processes at play in moraine formation and evolution through field observations and a numerical debris‐covered glacier model. The insulating effect of debris cover modifies glacier lengths and results in the development of ice‐cored moraines over multiple advances and thousands of years. Although ice cores can persist for several millennia, spatially variable ice core melt‐out contributes to moraine degradation and boulder destabilization, making it likely that the ¹⁰Be clock is reset on moraine boulders in these settings. Thus, exposure ages from ice‐cored moraines must be interpreted with caution. The oldest ages, after excluding samples with inheritance, provide the best estimates of initial moraine formation. Three Baffin Island moraines yield ¹⁰Be ages suggesting formation at 5.2, 4.6 and 3.5 ka, respectively, adding to a growing body of evidence for significant summer cooling millennia before the Little Ice Age.