These axes are fairly common in Skyrim, and one or more can be found in most settlements. Additionally, axes may rarely be found in the inventory of hunters roaming the wilds of Skyrim.
The following is a list of where axes can be found:
One axe sits outside Japhet's Folly Towers; upside-down atop a pile of logs, in one of the shacks that are on the island.
The second axe rests atop several crates, just inside the entrance to Japhet's Folly Towers that goes through the Sea Cave, at the bottom of the island.
Trivia
The woodcutter's axe is the fifth-weakest weapon in the game (tied with pickaxe and shiv). Only the iron dagger (when unimproved), knife, wooden sword (when unimproved), fork, and phantom sword rank lower in base damage.
The woodcutter's axe can be used to obtain an infinite amount of gold. The Dragonborn can use an axe to chop an infinite amount of firewood, which they can then sell to merchants.
After completion of the quest "Tending the Flames", Viarmo, headmaster of the Bards College in Solitude, may be found continually carrying around a woodcutter's axe. The reason for this is unknown.
Bugs
PC 360 PS3 While attempting to place an axe on a weapon rack, it seems to float horizontally, the axe's head facing the rack.
PS3 360 When activating the wood chopping block with the axe drawn, the Dragonborn will sheathe their weapon, then another axe will appear in the Dragoborn's hand, despite it clearly being sheathed at the Dragonborn's side. Once the animation is over, the second axe will disappear. This also happens when mining ore with a pickaxe.
360 Sometimes when dual wielding a dagger with the dagger in the main hand and the axe in the left hand, the axe will appear sheathed along with the dagger, with both weapons visible. However, the sheathing animation remains the same as any other left-hand weapon. The Dragonborn will simply lower their arms, and the axe will disappear from their hand.