The Frost Arrow rune for the Elemental arrow skill reads:
Fire a frost arrow that splits into multiple arrows after hitting its target
What I'd like to know is: can these split arrows split themselves? Can I create a chain reaction?
No, the Frost Arrow only splits the fist time. As you can read by its description: "Fire a frost arrow that splits into multiple arrows after hitting its target, dealing 160% weapon damage as Cold. Affected enemies have their movement speed slowed by 60% for 1 seconds." The initial Frost Arrow is the only one that will split.
Also you can see on this website : Frost Arrow: Turns into a frost arrow that explodes out conic damage from the back of the first target hit for 160% of weapon damage.