any suggestions for woodpecker?

If it's deemed to be a pest, it may fall under a different set of rules regarding shooting them. In IL, for example, squirrel season is only for a certain time from fall through winter. But if they're chewing on your house to get into your attic, they become 'pests' rather than 'game' and it's open season.

I have woodpeckers on my mulberry tree, and they're cute. But if they were tearing up my house, it would not be nearly as cute. Just sayin'.