The ability of general circulation models (GCMs) to reproduce the observed strong correlations of Eurasian snow extent in the fall to wave activity and Northern Annular Mode anomalies in the following winter is studied. The observed correlations have been hypothesized to involve two parts: a Rossby wave pulse generated in the troposphere in response to snow‐forced surface cooling and a coupled zonal‐mean stratosphere‐troposphere response to this Rossby wave pulse involving eddy mean flow interactions. It is found that all coupled ocean atmosphere GCMs used within the Coupled Model Intercomparison Project 3 (CMIP3) fail to capture the observed correlations. Using the CMIP3 GCMs and two versions of a particular GCM forced by prescribed sea surface temperatures, possible reasons for this are considered. The snow forcing, as represented in the spatial extent and interannual variability of snow cover area, is found to be reasonable although somewhat weak in the GCMs, as is the relationship between snow cover and the zonal‐mean circulation. However, the anomaly of eddy geopotential height associated with Eurasian snow cover anomalies is found to be too localized longitudinally in the GCMs. It is proposed that the reduced longitudinal scale of the snow‐forced Rossby wave pulse prevents it from propagating into the stratosphere, thus inhibiting the observed wave‐driven stratosphere‐troposphere response to the pulse.