Cocidius is quite Celtic, and is in fact, British or Brythonic. His name contains the word coch, still the word for red in Welsh today. This isn’t the only image of Cocidius; he was quite popular, especially with Romans. In the East, around Hadrian’s wall, he was associated with forests, and hunting. There’s an inscription to him at the old Roman fort in Ebchester (known to the Romans as Vindomara) that refers to him as Cocidius VERNOSTONUS, or “alder tree.” An altar in Risingham shows him hunting against a backdrop of trees (Green, Miranda. Dictionary of Celtic Myth and Legend. Thames and Hudson, 1992. 62).
In North and West Cumbria Cocidius was closely associated with the Roman god Mars. There are dedications to him at the old Roman fort of Birdoswald. At Bewcastle two silver repousse placques, complete with inscription, show Cocidius with spear and shield. There’s a reference in the Ravenna Cosmography to a fanum Cocidi that’s almost certainly Cocidius (Green, 62).
It’s quite possible that many of the unnamed deities along Hadrian’s Wall featuring hunting scenes, sometimes with horns, or the warrior with spear /sword and shield are Cocidius.