Woodcocks (Genus Scolopax) are unobtrusive smallish birds that forage during the evenings and nights, looking for worms and insects. They have a long, straight bill and their eyes are mounted toward the top of their skulls which affords them 360 degree vision.
The Eurasian Woodcock (Scolopax rusticola) is one of the more common species and found over large portions of Europe and into Asia. They frequent woodlands, scrublands, meadows and fields.
Woodcocks are mentioned as a creature the Vikings hunt, presumably to eat. In reality they are a popular gamebird, especially in Europe. The pin feathers have been used for artist's brushes in the past.
Stoick moves very fast to throw his shield in front of Hiccup when the Green Death explodes and send his talon straight at his unconscious son. This is because "Shooting woodcock with a bow and arrow develops very quick reflexes." In reality woodcock are a challenge to shoot with a gun, much less a bow and arrow.