Predicting how climate change will affect glacier and ice sheet flow speeds remains a large hurdle toward accurate sea level rise forecasting. Increases in surface melt rates are known to accelerate glacier flow in summer, whereas in winter, flow speeds are believed to be relatively invariant. Here we show that wintertime flow speeds on nearly all major glaciers throughout Alaska are not only variable but are inversely related to melt from preceding summers. For each additional meter of summertime melt, we observe an 11% decrease in wintertime velocity on glaciers of all sizes, geometries, climates, and bed types. This dynamic occurs because interannual differences in summertime melt affect how much water is retained in the subglacial system during winter. The ubiquity of the dynamic indicates it occurs globally on glaciers and ice sheets not frozen to their beds and thus constitutes a new mechanism affecting sea level rise projections.