Snow is a major determinant of forage availability for reindeer and caribou (Rangifer tarandus; hereafter Rangifer) in winter and is, consequently, a medium through which climate variation may influence population dynamics in this species. Periodic “icing” of winter ranges, where interludes of mild weather result in formation of crusted snow and basal ice that restrict access to forage, is held to be a cause of mass starvation, catastrophic declines in numbers, and even extirpation of local populations. It has been suggested that warming of the Arctic may result in increased frequency of winters with unfavorable snow and ice conditions, with serious consequences for Rangifer. This paper examines data on major declines in populations of Rangifer to determine the mechanism(s) of these events and the role of snow and ice conditions in them. Thirty‐one declines, involving numerical decreases between 25% and 99%, were identified in 12 populations. Declines were of two types: the negative phase of irruptive oscillations, mainly associated with populations introduced into new habitat, and numerical fluctuation in persistently unstable established populations. The mechanisms of decline differed widely in both categories, ranging from wholly mortality to almost wholly emigration. In all cases, the observed dynamics are best interpreted as a product of interaction between internal processes (density dependence) and the external abiotic conditions (density independence). The strength and the form of density independence, parameterized in terms of local weather or large‐scale climate, varies widely between populations, reflecting the enormous range of climate conditions across the circumpolar distribution of Rangifer. This complicates the search for abiotic components likely to be consistently important determinants of population growth in the species. There are few data demonstrating the presence of extensive hard snow or basal ice on ranges during winter(s) in which populations declined, and none confirming ice as a ubiquitous and potent agent in the dynamics of Rangifer. Instead, where the simultaneous effects of density‐dependent and density‐independent factors are examined across the full temporal record of dynamics, climatic conditions associated with increased amounts of snow or winter warming are generally found to enhance the abundance of animals, at least in established populations.