The properties of Banu al-Nadir were part of what Allah bestowed on His Apostle from what the Muslims has not ridden on horses or camels to get; so they belonged specially to the Messenger of Allah (ﷺ) who gave his family their annual contribution.
Ibn 'Abdah said: His family (ahlihi) and not the members of his houses (ahl baitihi) ; then applied what remained for horses and weapons in Allah's path.