There are some dove fields on gamelands and private farmlands will often have good populations during the winter season, you will have to scout a lot and then get permission. Most of the private land is leased out. I have never hunted up there, I'm south of that area. I rarely see snipe in any appreciable numbers.
On another forum/thread you were asking about deer hunting. Lots of deer up Williamston way, but again most of the land is private and leased. I think you have to apply for permits to hunt the Roanoke River gamelands for deer or waterfowl; not sure about the chances of getting drawn for one of those hunts. I'd inquire of the preserve operator you're booked with, I would think he'd know of a deer hunt you could get in on.
