Arctic Fur can only be skinned from beasts inhabited in Northrend and is very rare. There is not a proper method to farm Arctic Fur due to the rarity of the item. Farming Arctic Fur is based of grinding and luck. However with a high level character, skinning Anub’arak and Icehowl at the instance Trial of the Crusader may produce some Artic Fur. Other alternate method is to grind at Sholazar Basin, killing any beast as there is plenty in the zone.
See below for maps to farm Arctic Fur in WoW.