The Arctic Oscillation (AO) is the leading climate mode of sea level pressure (SLP) anomalies during cold season in the Northern Hemisphere. To a large extent, the atmospheric climate anomalies associated with positive and negative phases of the AO are opposite to each other, indicating linear impact. However, there is also significant nonlinear relationship between the AO and other winter climate variability. We investigate nonlinear impacts of the AO on surface air temperature (SAT) using reanalysis data and a multimillennial long climate simulation. It is found that SAT response to the AO, in terms of both spatial pattern and magnitude, is almost linear when the amplitude of the AO is moderate. However, the response becomes quite nonlinear as the amplitude of the AO becomes stronger. First, the pattern shift in SAT depends on AO phase and magnitude, and second, the SAT magnitude depends on AO phase. In particular, these nonlinearities are distinct over the North America and Eurasian Continent. Based on the analyses of model output, we suggest that the nonlinear zonal advection term is one of the critical components in generating nonlinear SAT response, particularly over the North America.