Using a coupled ocean-sea ice model of the pan-Arctic and North Atlantic Ocean, we investigate the response of the Arctic and subarctic thermohaline structure to seasonal extreme atmospheric forcing associated with the winter Arctic Oscillation (AO). During the positive phase of AO, significant surface cooling occurs in the Labrador Sea, but there is no substantial surface warming in the Barents Sea, i.e., no seesaw pattern in sea surface temperature (SST) anomaly between the Barents Sea and Labrador Sea. A possible explanation is that Arctic sea ice export into the Barents Sea melts locally and lowers the SST. However, a seesaw structure in subsurface (below the mixed layer: 40--100 m) water temperature anomaly between the two regions is found, exceeding the 95% significance level. Corresponding to the positive phase of the winter AO, a significant warming of the subsurface water in the Barents Sea and a concurrent cooling in the northwestern Labrador Sea are seen in the model results, which is analogous to the seesaw structure in both surface air temperature (SAT) and sea ice extent anomalies. The mechanism leading to the anomalous subsurface temperature seesaw is consistent with the northward advection of the warm Atlantic Water into the Barents Sea and the southward advection of the cold Arctic and sub-arctic water into the Labrador Sea from the David Strait and Baffin Bay. Hydrographic data are analyzed and the resulting temperature distribution supports this new finding.