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.