Laws may vary from state to state, but my understanding is that private land generally goes to the center of the road if it is one side only, even if the land owner doesn't use it. If the land is owned on both sides, than once you leave the access (the road) you are trespassing. Access is to the road only. Perhaps in some areas the barrow pit/ditch may be considered public access too, but you would want to be sure. I'm not sure how the animal would be off the property and you still accessing across it. Shooting an animal on or within a certain distance of the road is generally illegal in most places as well. I'll be curious to see if it pans out differently from area to area.