Will insurance cover the cost of squirrel damage to your siding?

No. Squirrel infestation is a maintenance issue and therefore is not covered under your homeowners insurance. I have the same problem and am about to have a squirrel shooting in my back yard. I will tell you a way to get rid of them as I did get them out of my attic. First you need to find the hole where they are getting into your house. Don't fix it yet until you get them out of the house. Purchase a few bottles of peppermint oil. Pour a little of the peppermint oil on cotton balls and put them all around your attic or where ever they are in your home. Be sure to cover the area well. After a little while you can close up the openings where they are gaining access to the home and seal it well. Squirrels hate peppermint for some reason and it works.