In this study, wood-plated Nomex honeycomb sandwich aircraft wing specimens with two different cell heights (10 and 30 mm) were prepared and subjected to low-velocity impact tests. To enhance the impact performance of the specimens, they were coated with a carbon nanotubes (CNT) reinforced epoxy matrix nanocomposite and the tests were repeated. The experiments were conducted in a laboratory environment at room temperature with energy values of 5 J, 10 J and 15 J using the drop tower test device. The damage mechanism in the structures were analyzed through numerical graphics obtained from the contact force–time, contact force–displacement and energy–time graphs. With CNT reinforcement, maximum displacement values improved by 10–29%, while an increase in cell height resulted in improvements of 19–33%. The maximum force increased by up to 61% in the 5 J and 15 J tests of both thin and thick specimens. The experiments were conducted to determine the effect of cell height on impact behavior, as well as the effectiveness of CNT reinforcement on impact damage reduction. CNT reinforcement led to a strength increase of up to 60%, which allowed for a reduction in cell height and therefore the wing/body thickness. It was also revealed that the inclusion of CNT reinforcement effectively reduced the damage to both the top plate and the honeycomb structure of the specimen. Severe damage modes such as upper plate fracture and cell crushing were significantly mitigated, while only matrix damage—considered tolerable and capable of preserving the integrity of the main structure—was observed.