Well yes, according to Mithrandir, the War of the Ring had begun at the time Thorin Oakenshield met Bilbo Baggins in The Shire. This means that the 12 other dwarves plus Thorin were involved in the War of the Ring. Furthermore, Dáin II Ironfoot of the nearby Iron Hill Dwarves also was involved in the Battle of the Five Armies.

Further, it is said that the Dwarves of the Red Mountain were involved in the war, fighting against Sauron.