The Arctic is warming much faster than the global average. This is known as Arctic Amplification and is caused by feedbacks in the local climate system. In this study, we explore a previously proposed hypothesis that an associated wind feedback in the Barents Sea could play an important role by increasing the warm water inflow into the Barents Sea. We find that the strong recent decrease in Barents Sea winter sea ice cover causes enhanced ocean-atmosphere heat flux and a local air temperature increase, thus a reduction in sea level pressure and a local cyclonic wind anomaly with eastward winds in the Barents Sea Opening. By investigating various reanalysis products and performing high-resolution perturbation experiments with the ocean and sea ice model FESOM2.1, we studied the impact of cyclonic atmospheric circulation changes on the warm Atlantic Water import into the Arctic via the Barents Sea and Fram Strait. We found that the observed wind changes do not significantly affect the warm water transport into the Barents Sea, which rejects the wind-feedback hypothesis. At the same time, the cyclonic wind anomalies in the Barents Sea increase the amount of Atlantic Water recirculating westwards in Fram Strait by a downslope shift of the West Spitsbergen Current, and thus reduce Atlantic Water reaching the Arctic basin via Fram Strait. The resulting warm-water anomaly in the Greenland Sea Gyre drives a local anticyclonic circulation anomaly.