A couple of Red-bellied woodpeckers have been paying regular visitors to my pecan tree this winter. Is this an indication of possible insect infestation on the tree? Is it possible they could damage the tree themselves? I have bird feeders there too and they seem to spend a lot of time there as well.
Are they "pecking" the tree trunk, or just roosting, hanging around and eating from the bird feeder? If they are spending time actually pecking holes in the trunk, then yes, most likely you have some sort of bug at work under the bark. Look for rows of holes in the side of the tree, and if you find any, check with your local Ag extension or a good nursery in town to find out what sort of bug you may be dealing with, and treat it appropriately.
While it certainly doesn't do any tree any good to have dozens (or hundreds) of weeping holes in it's trunk, the bigger problem is the chance that a fungus or other pests will inhabit the holes they have created while removing the beetle larvae or other pest they are digging out under the bark of the afflicted tree. The woodpeckers are actually doing a small good by removing the larvae, although if you do have a lot of action on a particular tree it can weaken it. However, if you get rid of whatever pest it is that they are eating, the birds should move on and find another tree to drill for food.