"namque sagitta lignea ferreae speciem habens nuntii loco viritim per omnes mitti, quoties repentina belli necessitas incidisset" Saxo Grammaticus, History of the Danes, Book V
"for a wooden arrow, having the appearance of being of iron, is to be sent man by man to every place as a message whenever the sudden necessity happened for war."
"Auðbjarnar konungr lét skera upp herör ok fara herboð um allt ríki sitt." Egils Saga, 3
" King Audbjorn allowed the war-arrow to be cut out and the war-summons to be sent around the entire kingdom."
Clearly Tolkien got the idea of the summons to war being an arrow from the Old Norse sources. I am sure he was familiar with both Egil's Saga and Saxo. It is interesting that he added the detail of the black arrow having the tip painted red. Maybe this is to separate it from the black arrow that Brand used to kill Smaug. Or to give its appearance an extra helping of horror since it appears to have been dipped in blood. Maybe we should vote on that.