Using nine chemistry-climate and eight associated no-chemistry models, we investigate the persistence and timing of cold episodes occurring in the Arctic and Antarctic stratosphere during the period 1980–2014. We find systematic differences in behavior between members of these model pairs. In a first group of chemistry models whose dynamical configurations mirror their no-chemistry counterparts, we find an increased persistence of such cold polar vortices, such that these cold episodes often start earlier and last longer, relative to the times of occurrence of the lowest temperatures. Also the date of occurrence of the lowest temperatures, both in the Arctic and the Antarctic, is often delayed by 1–3 weeks in chemistry models, versus their no-chemistry counterparts. This behavior exacerbates a widespread problem occurring in most or all models, a delayed occurrence, in the median, of the most anomalously cold day during such cold winters. In a second group of model pairs there are differences beyond just ozone chemistry. In particular, here the chemistry models feature more levels in the stratosphere, a raised model top, and differences in non-orographic gravity wave drag versus their no-chemistry counterparts. Such additional dynamical differences can completely mask the above influence of ozone chemistry. The results point toward a need to retune chemistry-climate models versus their no-chemistry counterparts.