How do I repair/prevent woodpecker holes in cedar siding?
Spraying inside the hole with spray foam such as great stuff then after letting it dry using some wood putty seems to be the best solution I've found. 

As for woodpeckers, there are typically two possible reasons they've decided to decimate your house. First is insects. This was our main problem, we had a bad carpenter bee problem in our fascia and the woodpeckers were burrowing to get the bees. Take care of the insects and eventually the woodpeckers will go away. Secondly, woodpeckers might have decided to call your house their home, if this is the case usually using deterrents can make them decide to call somewhere else home. The best thing I've found is aluminum foil. As they start to peck on a spot on your house, tape some aluminum foil over top the spot they were pecking. You'll probably only have to do this once or twice and they'll move on if there aren't insects. I have a cedar home and battled the little guys the first 3 years of owning it. 

You could shoot them with a pellet gun but they're protected under the migratory bird act making that illegal....