A timber dog
The timber dog in Market Lavington Museum is not an animal, but an iron hook used for moving logs.
A bit of research suggests that tools for this purpose might be called cant hooks, cant dogs or peaveys. They often seem to have long handles. The information we have on our record card says that a pole was inserted through the ring and then tree trunks could be moved by rolling them.
We have no expertise on this subject and would be delighted to receive a comment from someone who has experience of using such a tool.