Added the US Patent diagram.
The photo shows where the rein guides were located. In horse-harness lingo, they are called a "terret." Ignore the red-lettered "your item" in the horse-harness catalog scan.
The shape of a terret / rein guide's opening varies, sometimes merely a simple circle, sometimes a fancy geometric shape as we see on your find. But the distinctive shape of the lower part is always the same... a short thick threaded shaft with a disc-shaped collar (called a "stop") at the shaft's top. See the US Patent diagram for a variation of terret/rein-guide, below.
There are even fancier ones, called a "swinger" terret or fly-head terret. See the early-1900s advertizement, below.