Here is a link to West point hunting;
http://www.usma.army.mil/dcfa/activi...or/hunting.htm
In summary
If you are not in the military you can deer hunt on West Point property only if you have a doe tag for that deer management unit. You will have to get a West Point permit that costs about $10 and you MUST fill your doe tag first. After you check in your doe, they will issue a buck pass that will allow you to fill your N.Y. state buck tag on their land.
You have to sign in and out each day. The first week of gun season the military gets to sign in before dawn but the civilians have to wait until about 7am.