The main drivers of the continental Northern Hemisphere snow cover are investigated in the 1979-2014 period. Four observational datasets are used as are two large multi-model ensembles of atmosphere-only simulations with prescribed sea surface temperature (SST) and sea ice concentration (SIC). A first ensemble uses observed interannually varying SST and SIC conditions for 1979-2014, while a second ensemble is identical except for SIC with a repeated climatological cycle used. SST and external forcing typically explain 10 % to 25 % of the snow cover variance in model simulations, with a dominant forcing from the tropical and North Pacific SST during this period. In terms of the climate influence of the snow cover anomalies, both observations and models show no robust links between the November and April snow cover variability and the atmospheric circulation 1 month later. On the other hand, the first mode of Eurasian snow cover variability in January, with more extended snow over western Eurasia, is found to precede an atmospheric circulation pattern by 1 month, similar to a negative Arctic oscillation (AO). A decomposition of the variability in the model simulations shows that this relationship is mainly due to internal climate variability. Detailed outputs from one of the models indicate that the western Eurasia snow cover anomalies are preceded by a negative AO phase accompanied by a Ural blocking pattern and a stratospheric polar vortex weakening. The link between the AO and the snow cover variability is strongly related to the concomitant role of the stratospheric polar vortex, with the Eurasian snow cover acting as a positive feedback for the AO variability in winter. No robust influence of the SIC variability is found, as the sea ice loss in these simulations only drives an insignificant fraction of the snow cover anomalies, with few agreements among models.