There is a rich network of footpaths throughout the village and across the moors on either side of it. This is a map of the numbered footpaths in the parish. There is also a much more detailed interactive map on the SCC website. (And here are two more based around the Willows and Wetlands Centre: willow walk and permissive footpaths.)
Somerset County Council is responsible for the upkeep of footpaths, though a lot of work is done locally by our parish footpath warden Cecil Boobyer. If you encounter a problem with a footpath, drop Cecil an email, or report it directly on the SCC problems site.
You may also want to volunteer to befriend a footpath in exchange for a free pair of gloves and secateurs.