The study presents (a) a 44-year wintertime climatology of resolved gravity wave (GW) fluxes and associated zonal forcing in the extratropical stratosphere using ERA5, and (b) their composite evolution around gradual (final warming) and abrupt (sudden warming) transitions in the wintertime circulation. The connection between transformed Eulerian mean (TEM) equations and the linear GW pseudomomentum is leveraged to provide a glimpse of the importance of GW lateral propagation toward driving the wintertime stratospheric circulation by analyzing the relative contribution of the vertical vs. meridional flux convergence. The relative contribution from lateral propagation is found to be notable, especially in the Austral winter stratosphere where lateral (vertical) momentum flux convergence provides a peak climatological forcing of up to -0.5 (-3.5) m/s/day around 60oS at 40-45 km altitude. Prominent lateral propagation in the wintertime midlatitudes also contributes to the formation of a belt of GW activity in both hemispheres.