A diagnostic of Northern-Hemisphere winter extratropical stratosphere-troposphere interactions is presented to facilitate the study of stratosphere-troposphere coupling and to examine what might influence these interactions. The diagnostic is a multivariate EOF combining lower-stratospheric planetary wave activity flux in December with sea-level pressure in January. This EOF analysis captures a strong linkage between the vertical component of lower stratospheric wave activity over Eurasia and subsequent development of hemispheric-wide surface circulation anomalies, which are strongly related to the Northern Annular Mode (NAM). Wintertime stratosphere-troposphere events picked out by this diagnostic often have a precursor in autumn: years with large October snow extent over Eurasia feature strong wintertime upward-propagating planetary wave pulses, a weaker wintertime polar vortex, and high geopotential heights in the wintertime polar troposphere. This provides evidence for predictability of wintertime circulation for the extratropical Northern Hemisphere based on autumnal snow extent over Eurasia. We have operationally produced real-time winter forecasts for the US based on fall Eurasian snow cover and atmospheric anomalies for the past ten years. Operational forecasts have been expanded to include Europe, East Asia and all of Northern Asia. In addition, hindcasts have been produced for the winters 1972/73-2004/05. The operational forecasts continue to demonstrate skill, up through the most recent winter season. These snow-based forecasts appear to provide considerable additional information beyond the standard-ENSO based forecasts and even the most sophisticated dynamical models. Furthermore, a warming trend in global surface temperatures over the last forty years has been well established, consistent with anthropogenic increases in greenhouse gases. Over the last two decades, this trend appears to have accelerated. In contrast to this general behavior, however, we show that trends during the boreal cold months in the recent period have developed a marked asymmetry, with vigorous warming in October-December followed by a reversal to a neutral/cold trend in January-March. This observed asymmetry in the cold half of the boreal year is linked to a two-way stratosphere-troposphere interaction and a negative trend in the NAM index, which is strongest in the Northern Hemisphere during late winter and is related to variability in Eurasian land surface conditions during autumn. This link has been demonstrated for year- to-year variability and used to improve seasonal-timescale winter forecasts; however, this coupling is also shown to strongly modulate the warming trend, with implications for decadal-scale temperature projections.