Well, your right, but my brotheris an DEC cop and he was with me yesterday when I was checking the forums, and he stated to me that they can. Federal law over rules state or county laws and PRESIDENT BUSH signed that bill back in 2001 after 9-11 that says that cops can carry there firearms anywhere anytimein any state. So, that is a higher law then NY DEC laws so they can do that.
He told me that there is only3 places cops can't carry in the USA.
1. BEING IN A COURT ROOM, UNLESS ON DUTY. OFF DUTY NOT ALLOWED UNLESS COURT OFFICER ALLOWS IT.
2. ON AN AIRPLANE ONLY IF YOU HAVE PROPER PAPERWORK FROM DEPT. STATING OFFICAL BUSINESS OR FROM COURT. OTHERWISE ONLY FEDS. CAN CARRY ON BOARD AND PILOTS.
3. IN FEDERAL BUILDINGS THAT ALLOW LOCAL AND STATE POLICE TO CARRY FIREARMS.

anyways, i'm no lawyer just passing on what he told me. and if you check the law books, it does state NO firearms in the woods during bow season. but that's only for permit holding people.