A woodpecker symbolizes opportunity, creativity, and determination. It encourages individuals to use their intellect to overcome challenges and to appreciate the value of truth both in life and their spiritual future.
I feel like they do have a connection with Mars. Especially a large one like a Pileated woodpecker are like prehistoric. It feels like you are looking at a pterodactyl.
A woodpecker is a very industrious bird that uses it's beak in impressive speeds. I think in symbolism, it would mean hard, fast and well aimed work as a means to advancement. They are beautiful birds.
An interesting fact about woodpecker is that it have a long and bifurcate tongue that wrap completely around the skull until the base of the beak. The bird do that to absorb the shock and to protect from injury during high-speed pecking. It is in fact an interesting bird. In my country we call it the doctor of the trees.