This study examines pre-industrial control simulations from CMIP5 climate models in an effort to better understand the complex relationships between Arctic sea ice and the stratosphere, and between Arctic sea ice and cold winter temperatures over Eurasia. We present normalized regressions of Arctic sea-ice area against several atmospheric variables at extended lead and lag times. Statistically significant regressions are found at leads and lags, suggesting both atmospheric precursors of, and responses to, low sea ice; but generally, the regressions are stronger when the atmosphere leads sea ice, including a weaker polar stratospheric vortex indicated by positive polar cap height anomalies. Significant positive midlatitude eddy heat flux anomalies are also found to precede low sea ice. We argue that low sea ice and raised polar cap height are both a response to this enhanced midlatitude eddy heat flux. The so-called "warm Arctic, cold continents" anomaly pattern is present one to two months before low sea ice, but is absent in the months following low sea ice, suggesting that the Eurasian cooling and low sea ice are driven by similar processes. Lastly, our results suggest a dependence on the geographic region of low sea ice, with low Barents-Kara Sea ice correlated with a weakened polar stratospheric vortex, whilst low Sea of Okhotsk ice is correlated with a strengthened polar vortex. Overall, the results support a notion that the sea ice, polar stratospheric vortex and Eurasian surface temperatures collectively respond to large-scale changes in tropospheric circulation.