Nichols was born in Reading, Massachusetts, to Timothy Nichols and his wife Hannah Perkins. On July 7, 1761, Moses Nichols married Hannah Eaton of Lynn, Massachusetts. Colonel Nichols led a regiment of New Hampshire Militia (5th NH Militia Regt.) at the Battle of Bennington in 1777 and the Battle of Rhode Island in 1778. In 1780 he led his regiment to West Point where if formed part of the garrison. He attained the rank of Brigadier General.