House Dustin of Barrowton is a noble vassal house that holds fealty to House Stark of Winterfell (formerly House Bolton of the Dreadfort). They control Barrowton, a settlement in the Barrowlands, north of Blazewater Bay.
The only known member of House Dustin is the Lady of the house, Barbrey Ryswell.
While posing as a cupbearer to Tywin Lannister at Harrenhal, Arya Stark claims to be from Maidenpool, the seat of House Mooton. However, Arya is not able to identify House Mooton's sigil to Tywin. She admits to being from the North instead, claiming to be a stonemason's daughter from Barrowton. She describes House Dustin's sigil perfectly, convincing Tywin.
Tywin later criticizes Arya's pronunciation of "My lord." He says that she sounds high born but Arya counters that her mother served as a handmaid to Lady Dustin for many years and taught her how to speak properly.
In the books
In the A Song of Ice and Fire novels, House Dustin are the rulers of Barrowton. They have a vassal house of their own, House Stout of Goldgrass. House Dustin is ruled by Lady Barbrey Dustin, widow of Willam Dustin, who was one of the five Northmen killed in the Showdown at the Tower of Joy.
Brandon Stark was fostered during his youth at Barrowton by House Dustin and Barbrey Ryswell was besotted by him. She hoped to marry him, but this was dashed when he was betrothed to Catelyn Tully. Barbrey instead was left to marry Lord William Dustin, whose lands are on the eastern border of House Ryswell's. Following William's death at the end of the rebellion, it isn't clear if he had any heirs, as Lady Barbrey appears to rule Barrowton in his name. As a result, Lady Barbrey leads House Dustin to closely follow neighboring House Ryswell in political decisions, as its current lord, Rodrik, is her own father.
Lady Dustin holds a grudge against Eddard Stark for not bringing her husband's bones north with him so she could bury him at his ancestral home.
The Dustins, alongside the Ryswells, are the first to declare for House Bolton when Lord Roose is named Warden of the North, due to the kinship between them, and perhaps also because Lady Dustin hates the Starks. They are among the very few truly loyal vassals House Bolton has, while many of the other Northern houses deeply hate the Boltons and would gladly welcome a chance to destroy them (indeed some of them join Stannis for that reason). Even Ramsay knows to be careful around members of these two houses: with them, he is always courteous and smiling; what he is behind closed doors, however, is something else.
The Dustins and Ryswells assist the Bolton's to retake Moat Cailin: they surprise the ironborn on the Fever River, burning their longships; as a result, the ironborn garrison at the fortress is left without reinforcements and without means of escape.
Houses from the North