Robert McGhee (The Last Imaginary Place. A Human History of the Arctic World) doesn't think the original Arctic peoples were modern Western conservationists:
A... characteristic of Arctic peoples is the predilection for killing as many animals of prey species as possible, with the excess meat either stored for future use, shared with other groups or simply wasted. The casual and routine overkilling of animals on which people depend for their livelihood belies the romantic view of indigenous hunting peoples as natural conservationists, but it is undeniable that it occurs regularly. Overkilling, with no consideration of the biological consequences, has been consistent among Arctic hunters throughout history.
What does McGhee mean by overkilling: (a) simply that the hunters killed unnecessarily and didn't use everything that they killed; (b) that they improvidently drove animal populations to suboptimal levels (too few animals might drive the rate of kill per hour of pursuit undesirably low, for example); or (c) that animal populations were often driven to extinction? Storing for future use or sharing with others doesn't imply overharvest to me, but leaving meat on the ground to rot may (or may not).
In most cases the hunted species have not been seriously affected, since Arctic hunters are few and until the past century they did not possess weapons that were capable of making major inroads into animal populations. However, there is clear archaeological evidence that ancient hunters were capable of causing at least local extinctions. The muskoxen of Banks Island in Arctic Canada appear to have been wiped out at least twice, once about 3,000 years ago and again in the 1850s. The disappearance of the last surviving mammoths, on Wrangel Island far out in the Chukchi Sea, coincided with the appearance of human hunters on the island about 5,000 years ago. Krupnik [Arctic Adaptations: Native Whalers and Reindeer Herders of Northern Eurasia] argues that the extinction of many species of large animals in both Eurasia and North America at around the end of the Ice Age may implicate human hunters, who were living and working in Arctic-like environment and developing the hunting customs still practiced by Arctic hunters of the present day.
McGhee points out that many of these animal populations were migratory (A Land of Milk and Honey (If You Know Where to Look)). That would have made it hard for local bands of hunters to observe the complete life cycle of the animals and have prevented them from reaching an understanding of the biological relationship between harvest rates and population sizes. It would also have meant that anything not harvested when the animals came by was effectively - from the point of view of the band - wasted.
McGhee thinks overharvests were a result of the standard Arctic worldview:
Such hunting practices may seem simply reckless or heedless of consequences, but in fact they are intimately tied to the religions and worldviews of Arctic peoples, and these aspects of life are clearly relevant to any understanding of how Arctic hunting societies operate. In their traditional perception of the world and how it works, Arctic hunters generally see no link between overkilling and extinction, or even between overkilling and a drop in the population of prey animals. If any generalization can be made about the wide variety of beliefs held by individual northern societies, it is that killing of an animal is universally seen as a consensual act between hunter and hunted. The prey presents itself to be killed, selecting a hunter who is sufficiently skilled and knowledgeable as to how the body of the animal is to be treated. If the hunter follows the prescribed ritual designed to appease or please the soul of the dead animal, the creature is reborn in order to be killed again and provide for the needs of a hunter who has proven worthy of the kill. Animal populations decline or disappear not because they have been overhunted, but because hunters have not treated them with sufficient respect, and they have decided to avoid these hunters in the future. This view of the relationship between animals and humans appears to be well suited to the needs of people who must kill as often as possible in order to provide against the inevitable times of hunger that every Arctic hunter has experienced.
Edits: cleaned up spelling errors April 1, 2009.