This tool at Smith’s Tavern is a barking spud or barking iron, that was used to remove bark from a log. It is cast iron and appears to have been handmade by a blacksmith vs mass manufactured (but no maker’s mark).
It is a spoon or wedge-shaped iron bit that is worked underneath the bark to free it from the log. The idea is to wedge the barking spud into the layer between the bark and the wood, pushing around and along the log to loosen the bark. On a freshly cut green log, the bark will come off in big chunks. After the log dries out the bark can stick to the log making it difficult to use the barking spud, so it made sense to debark logs right after cutting the tree down.