At least in this area, those holes are from carpenter bees. Well, it is their fault. The woodpeckers are just the end result.
Carpenter bees drill holes into facia boards on cedar siding, perfectly circular ones, about 1/2 inch in diameter. Then they make a right turn and drill galleries (nests) parallel to the grain of the wood, just below the surface.
Woodpeckers find the hollow spots in the wood. They apparently can hear the difference between solid wood and those spots, so they tear out the nests and have dinner.
If you get rid of the carpenter bees and fill in the nests, the woodpeckers have no interest in your house. Other bugs can of course get in, but carpenter bees are the ones who like it up high. And unless you eliminate the bees, the woodpeckers will keep returning.
My approach is:
First dust the bees out of the nest. I don't want them returning to find another spot in my house. So I've got a duster that can squirt pesticide dust into the holes.
Once the nest is abandoned, I cut it open. On a ladder, a rotozip tool does a nice job of cutting opening up the galleries. If the bees have been too active, I'll remove and replace that section of facia board completely. But for a small nest, a rotozip tool is adequate.
Next, blow out the nest with an air line, removing any dead bees. A shop vac will also work.
Fill the galleries. Auto-body filler will work here, or a paintable caulk, or wood filler.
Re-paint.
Finally, spray each spring with an insecticide to dissuade the bees from returning.
If the problem is not carpenter bees, but perhaps carpenter ants, they like wet wood. Open the nest. A shop vac is good to remove the ants. Next, fix the reason why water is getting in, and replace/rebuild what was torn out.