Global climatic changes have been observed for all natural biomes, with the greatest impact in the permafrost zone. The short series of direct observations of air temperature and precipitation from meteorological stations for this territory make it difficult to use them in studies of the impact of climate change on forest and forest-tundra ecosystems, but only longer series of gridded data expand the temporal-spatial resolution of this analysis. We compared local and gridded air temperature, precipitation and vapor pressure deficit (VPD) data, analyzed the trends of their changes over the last century for three sites in the permafrost zone (YAK and TAY in Russia, and CAN in Canada), and estimated the effect of their variability on oxygen isotopes in the tree-ring cellulose (δ18Ocell) of three different species (Larix cajanderi Mayr, Larix gmelinii Rupr. Rupr and Piceaglauca (Moench) Voss). Climate trend analysis showed strong changes after the 1980s, and even more pronounced from 2000 to 2020. We revealed that δ18Ocell-YAK showed mixed signals of the July temperature (r = 0.49; p = 0.001), precipitation (r = −0.37; p = 0.02) and vapor pressure deficit (VPD) (r = 0.31; p = 0.02), while δ18Ocell-CAN captured longer March–May (r = 0.37, p = 0.001) and July (r = 0.32, p < 0.05) temperature signals as well as spring VPD (r = 0.54, p = 0.001). The δ18Ocell-TAY showed a significant correlation with air temperature in July (r = 0.23, p = 0.04) and VPD in March (r = −0.26, p = 0.03). The obtained eco-hydrological relationships indicate the importance of temperature and moisture to varying degrees, which can be explained by site- and species-specific differences.