I notified the Town about the confusing signs weeks ago, in this case based on confusion at Ruth Oliva Preserve after a local school teacher asked me for help since she was confused about the magic marker updates made to the signs.
I will bring this up again with them next week.
If you check the online map on the deer management page of the Town's website you can get information about the various properties and for AP it clearly says that it's open to both hunters and hikers and shows on the map where the hunters are supposed to be. Here's the link in case you have any difficulties navigating the Town's site:
http://tos.maps.arcgis.com/apps/OnePane/basicviewer/index.html?appid=e9aeb243715740f0a55024a739304fbf. You can pan and zoom the map to see all of the locations and should note that some of these are in fact closed to hikers.