The Göschenertal (Göschenen valley) is the type locality of the so‐called Göschenen Cold Phases I (~3–2.3 ka) and II (~1.8–1.1 ka). According to earlier studies, these Late Holocene climatic cooling periods were characterized by changes in vegetation and pronounced glacier advances. As a peculiarity, the Göschenen Cold Phase I was thought to be connected to a local surge‐type advance of the Chelengletscher (Chelen glacier) – an exceptional event of unparalleled dimension in the European Alps. Based on cosmogenic 10Be exposure ages from moraine boulders, we investigated the local glacier chronology. In contrast to former research, moraines at different positions within the Göschenen valley (central Swiss Alps) have been dated to the Younger Dryas and the Early Holocene. This questions the applicability of palaeo‐Equilibrium Line Altitude (ELA) calculations for stadial attributions without additional numerical age constraints. Furthermore, we have found compelling evidence that the proposed non‐climatic glacier advance attributed to the Göschenen Cold Phase I did not occur. The present results, along with a reappraisal of the original study, question the scientific reliability and the glaciological definition of the Göschenen Cold Phases as glacier advances that clearly exceeded the Little Ice Age positions. While our data do not exclude potential changes in climate and vegetation, we nonetheless show that the Göschenen Cold Phases are not suitable as reference stadials in the system of Alpine Holocene glacier fluctuations.