SummaryUnderstanding how climate change will affect animal population dynamics remains a major challenge, especially in long‐distant migrants exposed to different climatic regimes throughout their annual cycle.We evaluated the effect of temperature throughout the annual cycle on demographic parameters (age‐specific survival and recruitment, breeding propensity and fecundity) of the greater snow goose (Chen caerulescens atlanticaL.), an arctic‐nesting species. As this is a hunted species, we used the theory of exploited populations to estimate hunting mortality separately from natural mortality in order to evaluate climatic effects only on the latter form of mortality.Our analysis was based on a 22‐year marking study (n = 27 150 females) and included live recaptures at the breeding colony and dead recoveries from hunters. We tested the effect of climatic covariates by applying a procedure that accounts for unexplained environmental variation in the demographic parameter to a multistate capture–mark–recapture recruitment model.Breeding propensity, clutch size and hatching probability all increased with high temperatures on the breeding grounds. First‐year survival to natural causes of mortality increased when temperature was high at the end of the summer, whereas adult survival was not affected by temperature. On the contrary, accession to reproduction decreased with warmer climatic conditions during the non‐breeding season.Survival was strongly negatively related to hunting mortality in adults, as expected, but not in first‐year birds, which suggests the possibility of compensation between natural and hunting mortality in the latter group.We show that events occurring both at and away from the breeding ground can affect the demography of migratory birds, either directly or through carryover effects, and sometimes in opposite ways. This highlights the need to account for the whole life cycle of an animal when attempting to project the response of populations to future climatic changes.