Accumulating evidence is suggesting more frequent tropical-to-temperate transitions than previously thought. This raises the possibility that biome transitions could be facilitated by precursor traits. A wealth of ecological, genetic and physiological evidence suggests overlap between drought and frost stress responses, but the origin of this overlap, i.e. the evolution of these responses relative to each other, is poorly known. Here, we test whether adaptation to frost and/or severe winters in grasses (Poaceae) was facilitated by ancestral adaptation to drought. We used occurrence patterns across Köppen-Geiger climate zones to classify species as drought, frost and/or winter tolerant, followed by comparative analyses. Ancestral state reconstructions revealed different evolutionary trajectories in different clades, suggesting both drought-first and frost-first scenarios. A model of correlated evolution was not supported when transition rate heterogeneity was taken into account or compared to traits simulated under independent evolution. Our findings provide some support for ancestral drought tolerance facilitating transitions to cold, temperate biomes, at least in some clades. Different scenarios in different clades is consistent with present-day grasses being either cold or drought specialists, possibly as a consequence of trade-offs between different stress tolerance responses.