Despite rapid global warming, Eurasia experienced unusual winter cooling from around 1992-2012, whose cause is still debated. By analyzing observations and model simulations, we show that the winter cooling from 1992 to 2012, as well as the enhanced winter warming from 1971-1991, over Eurasia partly resulted from internally-generated multidecadal variations related to variations in sea ice cover (SIC) and surface air temperature (Tas) over the Barents-Kara Seas (BKS). The BKS SIC and Tas variations concur with a multidecadal trend towards an anticyclonic (cyclonic) anomaly circulation over the Ural Mountains during 1992-2012 (1971-1991) that advected cold (warm) air from the Arctic (southwest Eurasia) into central Asia, contributing to the cooling (warming) over most Eurasia during 1992-2012 (1971-1991). These multidecadal variations in BKS SIC and Tas largely disappear, and the associated anomaly circulation and its influence on central Eurasia (CE) weaken when sea ice-air interactions are absent, although reduced multidecadal cooling over CE still exists in simulations without Arctic sea ice-air coupling. Because of the 10-20 day lifetime of Ural blocking, daily Arctic sea ice-air interactions, which are absent in all simulations with prescribed sea ice, are crucial for models to realistically simulate Ural blocking events and their decadal frequency and other changes that connect the BKS and CE Tas anomalies. BKS multidecadal warming is insufficient to induce CE cooling when Arctic sea ice-air interactions are turned off in our simulations. In contrast to the multidecadal BKS sea-ice decline, global-warming induced long-term sea-ice loss does not cause cooling over CE, likely due to other associated changes. As sea ice continues to melt away, its ability to cause such multidecadal variations and cooling over Eurasia will diminish.