Ember : a novel / Brock Adams.

Enhanced descriptions from Syndetics:

Three years ago, the sun began to die. In a desperate attempt to reignite the failing star, the United States had joined the rest of the planet in unloading its nuclear arsenal at the flickering ember. The missiles burst from silos in Wyoming and Bangladesh, cocooning the earth in tendrils of smoke as they began their two-and-a-half year journey into space. When they finally reach their target, it's thirty degrees in July and getting colder. Lisa and her husband, Guy, sit shivering on a Southern hilltop, watching as humanity's last hope at survival shimmers faintly...and then disappears below the horizon.
A group of militant rebels called the Minutemen take advantage of the ensuing chaos to knock out power grids, cloaking the freezing earth in near darkness. Seizing control. To escape this ruthless new world order, Lisa and Guy join a reluctant band of refugees crossing the snow-covered South in search of shelter and answers. From an icy parking lot in Atlanta to the Minutemen's makeshift headquarters at Asheville's Biltmore Estate, only one thing is certain: in a world with little light, nothing is guaranteed--least of all survival.

Ember is the 2016 winner of the South Carolina First Novel Prize as judged by novelist Bridgett M. Davis.