I would immagine that you are right Dave. Just to go sideways on this one, in Hank Wangford's excellent book "The Lost Cowboys" (or it might be "In Search of The Los Cowboys") he tells us that the "typical" Mexican trumpet was another Hollywood invention because the trumpet could be better picked up by the early microphones than fiddles.

I would think that carying a guitar on horseback would be neither good for the cowboy, horse or the guitar.