Several studies suggest that the Siberian snow cover in fall is a source of predictability of the Arctic Oscillation (AO) in winter. Although a plausible dynamical mechanism was proposed, the robustness of this relationship was recently challenged. Here we use two atmospheric reanalyses to revisit the snow‐AO relationship and its modulation across the whole twentieth century. While our results support a stratospheric pathway mechanism, they show that the snow‐AO relationship has only emerged in the 1970s and should be rather analyzed as a contrasted multidecadal behavior of the North Atlantic Oscillation (NAO) and Pacific North America pattern. They confirm that the quasi‐biennial oscillation is a plausible candidate for the modulation of the snow‐(N)AO relationship across the twentieth century, but they further show that this modulation might be a purely stochastic effect. Therefore, they emphasize the limitations of any empirical prediction of the (N)AO only based on snow and/or sea ice predictors.