Dear Barbara,
I don't know about hairy/downy woodpeckers in particular, but marrow is rich in nutrition and birds are clever at figuring out ways to get nourishment...I found two references online to observations of a pileated woodpecker scavenging a carcass and a golden-fronted woodpecker eating a mouse and feeding bits of it to its young; and bearded vultures (lammergeiers) feed heavily on bone marrow and even drop big bones onto rocks to smash 'em open to get at it. If bluetits in England are ingenious enough to figure out how to get into a milk bottle to skim the cream, I can't imagine that a woodpecker would be less able to figure out how to pillage a carcass!

cwilsdon at earthlink.net
Seattle WA