Black Bear

Found, in modern times, in mainly North America. The black bear tends to inhabit northern climes characterised by cold winters, forests, rivers, and mountains. Well known for being one of the larges hibernating species in the world. Black bears are clever animals that will eat anything the need to survive, which includes jut about anything. Their diet varies from berries, to fish, to meat, to honey. It seems Mr Milne got his inspiration from reality. 
The largest populations of black bears are presently to be found in western Canada. The harsh landscape and climate my be reasons for the lack of human settlement. However bears of many kinds can be found here, provided one knows what to look for. Like most bears the spend the year from spring to autumn fishing, foraging, and hunting. Both for immediate survival but also for the winter. As, like many animals who live in their habitat. They hibernate for the winter, and so a substantial fat reserve is essential for survival. Nonetheless it's not recommended that one calls a black bear, or any bear, fat. A somewhat eccentric English ursinologist once set out from the University of Toronto to do exactly this in 1927. He hasn't been seen since and, whatever the truth of the matter, he is due to be declared legally dead in July.
That said black bears are not usually a threat to humans, who they will leave alone provided they do not see humans as a threat; or dinner. They also have the distinction, presumably unwelcome to the bears themselves, of being the main material for the distinctive headwear of the foot regiments of the Household Divisions. Thus making them a valuable prey for human hunters. Though it takes considerable skill and bravery to catch such a beast, and the vastness of the Canadian interior all but guarantees these hardy animals will survive for many generations more.