Two types of permits in NY, premises, and concealed carry. Although I recently heard that a carry permit covers both concealed and non-concealed. But if you are not in the woods, why in the world would you NOT conceal it? "Hey bad guys, here is where I keep my gun, so you can disarm me!" Also, it is not worth alarming the gun-hating types, so in public, I hide it. When in the woods, I could care less.
That whole "hunting and target" restrictions was, in my mind, unconstitutional Bull Excrement. Aren't you glad Mulroy is off the bench?