Unfortunately I have not done much research on the Horn connection to my Chamber's lineage. Because Richard married Jincy Chambers in Allen Co KY where Jincy was born and raised by her half-sister Lucy Chambers Oliver - both parents having died before 1827. There was a large group of folks from Allen Co, including the Horn's ( who had migrated to Logan Co before 1850), who migrated to the Greene, Maries, Cass, and Saline Co MO about 1854.
My gggrandfather John Shelby Oliver returned with one other brother to southern KY, but the rest remained. John Shelby Oliver served with Faulkner's Regiment, a confederate unit under Nathan Bedford Forrest. I don't know if he communicated with his cousin Given's Horne, as my uncle,in his zealous youth, cleaned out and destroyed all the papers in the attic of the house he purchased that belonged to John Shelby, in the 1950's.
I feel that Richard is connected to the Allen County KY Horn's but haven't delved into that family, except for having come across an obit for Richard's sister Priscilla Horn Morris, wife of Daniel, who died in Warren Co KY 1877. I have not find any information on her or other siblings of Richard.