The general retreat of Arctic sea ice is overlaid by large year-to-year variability. In winter, sea ice loss and variability are currently most pronounced in the Barents Sea, primarily due to variable ocean heat transport from the Atlantic. As the loss of winter Arctic sea ice is expected to continue and the sea ice edge retreats deeper into the Arctic Ocean, other regions will experience increased sea-ice variability until essentially ice-free. However, it remains to be established to what extent future winter sea ice loss beyond the Barents Sea is facilitated by ocean heat transport. To answer this question, we analyze and contrast the present and future regional impact of Pacific and Atlantic ocean heat transport on the winter Arctic sea ice cover using simulations from seven single-model large ensembles. We find strong model agreement for an expanding influence of ocean heat transport through the Bering Strait and the Barents Sea under continued sea ice retreat. Model differences can be related to mean volume transport and inflow temperature, mean sea ice state, and upper ocean stratification. Our work highlights the increasing importance of the Pacific and Atlantic water inflows to the Arctic Ocean and indicates that their future influence regions will be separated by the Lomonosov Ridge.