I like the laws in NY. There is no right to enter someones land without permission posted or not. If you do you are tresspassing. Even a game warden can not come on your property for the purpose of pursuing someones wounded animal. A warden can enter private propertyoutside of what is called the curtilage only for the purpose of checking licenceses of hunters envolved in a hunt or if there is probable cause envovinga violation. The curtilage is the area of land occupied by a dwelling and its yard and outbuildings, actually enclosed or considered as enclosed. A warden needs a warrant to enter your curtilage just like any other cop. There are a couple of exceptions to allow for extreme situations like if a crime is in progress or to prevent loss of life or injury. I'm not sure about the specifics of the exceptions but finding somebody's deer certainly isn't one of them.

Imo, finding a wounded or downed deer is no reason to violate private property rights.