Climate change will cause a substantial future greenhouse gas release from warming and thawing permafrost-affected soils to the atmosphere enabling a positive feedback mechanism. Increasing the population density of big herbivores in northern high-latitude ecosystems will increase snow density and hence decrease the insulation strength of snow during winter. As a consequence, theoretically 80% of current permafrost-affected soils (<10 m) is projected to remain until 2100 even when assuming a strong warming using the Representative Concentration Pathway 8.5. Importantly, permafrost temperature is estimated to remain below -4<degrees>C on average after increasing herbivore population density. Such ecosystem management practices would be therefore theoretically an important additional climate change mitigation strategy. Our results also highlight the importance of new field experiments and observations, and the integration of fauna dynamics into complex Earth System models, in order to reliably project future ecosystem functions and climate.