Closely related species often use the same genes to adapt to similar environments. However, we know little about why such genes possess increased adaptive potential and whether this is conserved across deeper evolutionary lineages. Adaptation to climate presents a natural laboratory to test these ideas, as even distantly related species must contend with similar stresses. Here, we re-analyse genomic data from thousands of individuals from 25 plant species as diverged as lodgepole pine and Arabidopsis (~300 Myr). We test for genetic repeatability based on within-species associations between allele frequencies in genes and variation in 21 climate variables. Our results demonstrate significant statistical evidence for genetic repeatability across deep time that is not expected under randomness, identifying a suite of 108 gene families (orthogroups) and gene functions that repeatedly drive local adaptation to climate. This set includes many orthogroups with well-known functions in abiotic stress response. Using gene co-expression networks to quantify pleiotropy, we find that orthogroups with stronger evidence for repeatability exhibit greater network centrality and broader expression across tissues (higher pleiotropy), contrary to the 'cost of complexity' theory. These gene families may be important in helping wild and crop species cope with future climate change, representing important candidates for future study.