No Saddlebreds in my hunt but I routinely trail ride with two friends and their Saddlebreds. They are terrific geldings. One of them will chase/herd cattle as well as any Foundation Quarter horse.
As a sidenote back in the early 80’s I visited with Jan Dickenson at her farm next to a barn where I was riding in Virginia. She was retired-career military, wrote a book or two and an avid fox hunter at an earlier time. At this point in her life she was investing herself in the dressage world but could not afford to import a Warmblood from Europe. Her solution, she used Saddlebreds that suited the way of going she needed. They had the neck set, strong shoulders, short back and athleticism she wanted without the price tag. I thought that was very cool.