Unless you want to stand outside on patrol at all hours, there's not much you can do about the woodpeckers in your area. Sure, you can hope that your local woodpeckers will stick to pecking at the local trees, but if they do come for your wood siding, you're going to need to know how to fill in those holes.
Buy some Bondo Body Filler at your local auto parts store. It's a product designed for car dents, but it can be used to patch up all kinds of different holes. Mix the contents of both filler tubes together until they form a pink paste. Let the paste harden, but don't let it get so hard that you can't apply it inside of your woodpecker holes.
Fill the woodpecker holes with the hardened paste, using a putty knife. Put enough paste in the holes so that it sticks out a little more than the original wood siding.
Let the paste dry for a few hours and then sand it down until it's even with the wood siding.
Cover each filled-in hole with the same product you used to finish your original wood siding. Whether it's a primer, paint, or a stain, you'll have your siding looking like new until the next time those pesky woodpeckers come around.