Pan. He was also the god of nature in general.
Pan was the Greek god. His Roman counterpart was Faunus.
Nemestrinus
Diana was the Roman God who was the guardian of wild beasts, horses, and domesticated animals.
Faunus
A Roman god of Fields and Woods
I think you might be thinking of Faunus, which is the Roman counterpart to the Greek Pan, but they are only gods of the woods. There is no Greek or Roman deity associated with the concept of mischief.
The Greek god of nature, and the wild was Pan. He was a creature known as a satyr. His Roman counterpart was the god Faunus.
Diana was the Roman goddess of the hunt and the wilderness. Her Greek counterpart was Artemis.
Freyr is the Norse god of the woods. Freya is his female counterpart and is the goddess of the woods.
The Roman God Neptune is the God of the sea.
Pan god of the wild
the god of wild is Pan
There are actually two roman deities who were associated with the woods and the fields. The first was Faunus, who specifically presided over the forest. He would even grant anyone who slept within the boundaries of his woods a prophetic dream. Silvanus is the god who is said to have governed the countryside, including the forest, farmlands, hunting, and herding cattle. Both of these gods were generally respected by the lower class farmers of Rome rather than those of the upper class.
Because he is the god of nature.