I am building in a wooded area. Could I have a problem with carpenter ants?

Possibly, if you build your nest in ant territory they might build their nests in yours. Unlike termites, carpenter ants do not eat wood, they just burrow in it, and the softer the wood, the easier the work. That's why they like moist, rotting limbs and stumps.
Given the opportunity, carpenter ants may also tunnel into the foam insulation in wall and roof panels as they will in fiberglass and cellulose insulations. The resulting damage is often negligible, but left unchecked, these ants can dig out enough insulation to reduce the thermal effectiveness of the panel and conceivably affect its structural performance.
Preventing carpenter ant infestation in any structure is easier than curing it and prevention is most easily done during construction. Use pressure treated lumber for the sill and other areas subject to dampness. Leave a 2-foot buffer zone between the house and surrounding vegetation, and protect against "aerial attack" by trimming back any overhanging tree limbs. Seal and periodically check all potential entry points. Clear away any natural nesting materials such as dead trees and downed limbs, and store firewood well away from the house.
In areas that are particularly prone to ant problems such as heavily wooded areas or low shaded areas where the ground stays damp, consider treating the foundation with a long-acting pesticide prior to backfilling and install termite shield under the sill. Consult a local treatment expert for further recommendations on long term control methods for your area.
Be equally inhospitable inside the house. Ants don't eat wood or insulation; they eat things like food scraps, garbage and insects, and will be much less attracted to a clean house.
Control indoor humidity with an active ventilation system. Excessive humidity causes condensation which can soon result in moist, rotting wood - just what ants like.