Your initial impression was correct. It's a harmless eastern garter snake. In the east they generally feed on fish, frogs, salamanders, earthworms & toads. That toad's not stuck, its an almost finished meal.

Ring necks are also in your area, but they have a "ring around the collar". The ring is yellow or orange and it's the only marking on the snakes back. The top of the body is bluish grey, & the belly is orange or yellow with tiny black spots.