There is evidence of climate hormesis (low-dose stimulation and high-dose inhibition by climate change-related stressors), the adaptive response of cells and organisms to moderate, intermittent stress, at community and ecosystem levels, including forest ecosystems with low levels of climate stressors. However, the role of climate hormesis in carbon sequestration by forests and its effects on global processes in the biosphere remains poorly understood. This paper examines this issue based on data for forests of various biomes. The analysis has shown that soil and vegetation are the main carbon pools in forests, which sequester carbon in humus and woody organic matter. Low dose climate stressors (i.e., moderate stressors related to climate change), through hormetic stimulation of growth and photosynthesis, can increase forest productivity and carbon sequestration by ensuring long-term carbon conservation in wood. Climate hormesis can potentially enhance soil carbon stocks by increasing carbon runoff from vegetation. This may have a reverse stimulating effect on the productivity of trees by increasing available minerals, especially nitrogen. At the biosphere level, climate hormesis of forest ecosystems may be a mechanism of self-regulation, compensating for or at least restraining the pace of climate change, increasing the chances of biomes and ecosystems for successful adaptation. However, anthropogenic activities disrupt this mechanism and the buffer capacities of forests in the face of climate change, reducing their area, especially primary forests and their biological diversity. This review demonstrates the importance of hormesis for studying the effects of climate stressors on carbon sequestration by forests and may be used to enhance their buffering properties.