"NC mountains" is a vague area...I live there, (used to in winter, now just 7 months a year). If you are climbing very steep, shaded roads, above 4500/5,000 feet in far western NC or 'north west NC', it will be an experience. If you are rolling around Asheville or the Piedmont, not so much problem.
I would skip the chains, but go easy, use hill descent on steep declines and, I hope you have more than just Miami Driving experience.
Those tires are just ok for basic flatland winter driving, but only dedicated snow tires work on the common very steep inclines/declines found in Waynesville, Blowing Rock, Boone, etc. I would stick to main roads...
GL, mD