From documents about the park we know that Olmsted and Vaux intended to honor those who brought wood related materials, wood, turpentine, charcoal, etc. into the city. But a woodsman is so much more than that. Masters of the woods, self sufficient inhabitants of the forest which gave them their livelihoods. In their spirit you will need to solve a different type of puzzle: finding everything you need to survive... within Central Park itself.
Wilderness survivalists will tell you that the human body has three basic needs for survival: food, water and shelter. Finding these things will require a combination of skills that any woodsman would possess. Map skills, the ability to ID plants, and a hunter's instinct. But if you can find everything you need then you'll be able to find the geocacher's 4th requirement for survival: a cache.
First: Water. Assuming that the water flows from west to east, and that the center of the stone wall marks the boundary of the park, find the point at which Montayne's Rivulet enters Central Park. You are 3008' away.
Second: Food. Beyond what is provided by the vendors there are over 120 edible plants available for forage if you can identify them. A monument to a great American stands in a grove of apple and crabapple trees, both of which bear edible fruit. The statue stands near a monument whose shape was echoed in another monument, in another city. That distant monument honored the person who this man served under. Standing at the back of the statue you are 3088' away.
And your final need: Shelter. Luckily Central Park provides quite a bit of shelter. But if you are going to survive you might as well survive in style, eh? Find the park's oldest standing structure, from it's central point you are 4118' away.
The first 2 finders will receive a gift that will be helpful for your survival in the city.
Woodsmans Gate was nominated as one of the best of Manhattan caches in 2010 by the Metro New York Geocaching Society!