Goats would love eating in woodland but the woodland may not love them. Goats strip bark off trees and can kill them. Normal stock fencing with an electric wire. Mine just have an electric wires so can move grazing areas, so possible to use round trees to protect them depending on layout. They need access to shelter with hay when raining /bad weather. Mine only eat nettles at the right stage normally strip the leaves when they are tall and flowering.
Goats love eating branches and leaves also like stripping the bark off trees so can kill a tree you may need to put tree guards or supervise them to stop them stripping the bark. Standing on their hind legs can reach 6ft for a tasty bit. Mine would go for the branches first before the nettles brambles which they do like as well .