There may not have been any direct Masonic link. In the late 1800's there were literally hundreds, if not thousands, of fraternal orders and societies, and many referred to their local chapters and meeting places as "lodges." However, there may well have been some Masonic influence for a couple of reasons. First, many of the other, newer orders borrowed heavily from Masonic rituals and traditions in creating their own. Second, it was common for men to belong to a number of such orders simultaneously: a Mason might also belong to the Odd Fellows, Knights of Pythias, etc.
Also, there is some indication that the Knights of the Horse-Shoe were around at least as late as the Civil War and fervent supporters of the Confederate cause. "Beechenbrook : A Rhyme of the War" by Margaret J. Preston, published in 1865, contains the line, "For ye're 'Knights of the Horse-Shoe'?ye're Sons of the South!" So, who knows? Maybe some Knights of the Horse-Shoe went West with the war as far as Arkansas, and in time became so "Independent" that they threw the "Shoe"!