If you are licensed to carry in the state, yes. This was a federal law change last year. Still, check with state law enforcement.
The Federal law change was for lands under the control of the National Park Service. National Forests are under the control of the US Forest Service and were unaffected by the new Federal law.
Follow up to my question, should anyone else want to know in the future. I spoke with a Forest Ranger assigned to that Forest, she stated it is allowed. As long as NYS laws are followed(conceal only, permit, and so on). I would still advise you to call if you plan to vist. (607)-546-4470.