The presence of snow over broad land surface regions has been shown to not only suppress local surface temperatures, but also influence various remote climate phenomena. However, the specific mechanisms and snow anomaly characteristics which produce this response are still not well understood. In this study, large-ensemble general circulation model (GCM) experiments are performed to investigate the sensitivity of the atmospheric response to snow cover vs. snow depth anomalies, and the relevant surface thermodynamic processes involved. Realistic, observation-based, autumn-winter snow forcings over Siberia are developed and applied as model boundary conditions, to evaluate the climate response to (1) comprehensive snow forcings including snow cover and snow depth components, (2) snow cover only forcings, and (3) snow forcings in the absence of a surface albedo response. Results indicate that snow cover extent anomalies are not the only significant contributor to the local temperature response; snow depth anomalies are shown to have a comparable effect. Furthermore, the albedo effect is not the predominant thermodynamic mechanism; processes related to the insulative properties of the snowpack (e.g., thermal conductivity and latent heat flux) are also involved. Lastly, we find that realistic snow cover and snow depth anomalies acting in conjunction are required to produce a local temperature response which is strong enough to distinctly modulate the winter Arctic Oscillation (AO) mode as shown in previous studies. Such a detailed understanding of the atmospheric sensitivity to snow anomaly characteristics is beneficial for effectively utilizing any potential climate predictability contained in snow anomaly signals.