As a whole, North Carolina was not a bastion of arts and culture during this time, while there were certain things that arose to culturally distinguish North Carolina at this time, it produced very little art or writings that defined its era or its culture at the time.
The most prominent form of artistic expression in North Carolina during this time was pottery. North Carolina’s soil was, and still is incredibly rich with clay. The Native Americans used to have methods of using it to create pots and bowls, and the tradition remained strong in North Carolina following their decline, and remains strong today. In North Carolina families of potters would join together in communities in order to develop objects primarily for food storage and preservation. One thing that set the potters of North Carolina apart however, was their attitude towards the pottery that they were making. Very few of them considered it to be art, and they produced their pottery solely for personal reasons. Occasionally they would sell their pottery, or maybe engrave some waves or flowers onto it, but actions like this were the exception rather than the rule.
The other unique art form of this time in North Carolina was its architecture. While the lower class (unskilled craftsmen, small-time farmers etc.) had pretty standard dwellings for this age, the upper class embraced a different architectural style. The most common style of architecture in North Carolina at this time was the Georgian style. The Georgian style represented a disdain for the incredibly detailed and ornate architecture that was prominent in England, and instead focused on very basic and symmetrical attributes in its design. Because of the popularity of this style all throughout North Carolina, the houses of many federal buildings and old houses (particularly those of wealthy plantation owners) are quite bland in nature, and they were intended to appear that way.
The largest culture at this time was undoubtedly that of the Scotch-Irish, with their massive immigration to the region during this time, they had an enormous impact on the culture of the region. The most influential thing that they brought with them was undoubtedly their Presbyterian faith, although it did occasionally clash with the Calvinist and Quaker beliefs that were also strong in North Carolina, it was a dominant influence in shaping the culture of North Carolina as a whole. Even the agricultural techniques employed in North Carolina at this time were brought over by the Scotch-Irish.
So overall, North Carolina did very little to contribute to the cultural identity of the United States as a whole in this age, while certain members of the state did some things to culturally set themselves apart from their peers, North Carolina as a whole was not a culturally significant state.