Unless a fee is charged by the landowner for permission to hunt, a NY statute specifically exempts landowners who grant permission to hunt their land, so long as they receive no compensation in return.

http://ecommons.library.cornell.edu/bitstream/1813/3921/2/Natural%20Resources%20Sea%20Grant%20-%20Recreation%20Access%20and%20Liability.pdf

Let's try this again:

By a statute passed in 1956, now known as section 9-103 of the New York General Obligations Law, the New York legislature limited the liability of landowners who grant permission to recreationists to use their land without compensation. The broad limitation of liability is described here:

http://ecommons.library.cornell.edu/bitstream/1813/3921/2/Natural%20Resources%20Sea%20Grant%20-%20Recreation%20Access%20and%20Liability.pdf

I would argue that if you define the deer as a problem and allow hunting on your property you are receiving value and thereby are being compensated...