Arctic Oscillation (AO) is the main source of climate variability in the extratropical regions. The years with positive AO are associated with warmer mid-latitudes and colder polar regions than normal, and vice versa for negative AO. Snow cover (SC) has been shown to have an impact on the temperature through albedo interactions, and the interactions of snow and atmospheric circulation during winter months. Previous studies have shown that while AO is reproduced as the leading pattern, the amplitude and phase of AO seem to be poorly reproduced in the models. This study investigated the connection between November SC extent and December AO, as the potential source of model inaccuracy. While some of the models reproduce both AO and snow well, only three models represent the connection between AO and snow accurately. This study proposes that the mechanism of the connection might be in the snow cover intensifying the troposphere-stratosphere interactions and propagation of the atmospheric waves. We identify that thinning of atmospheric layers, combined with already existing troughs, can lead to amplification of wavenumber-1, intensifying AO. We show that the models which represent the correlations between snow and AO well, also simulate the proposed physical processes. The thinning of the atmospheric layers leads to upward Eliassen-Palm flux propagation to the stratosphere, which is shown in both the observational data and the model simulations from well-performing models. However, the connection between November snow cover and the daily geopotential field, specifically vertical propagation of the planetary waves, is poorly simulated in the models, which is potentially one of causes of bad performance of the models in simulating AO accurately.