leeneia, our dad always told us to talk to the horses when we were on their sides or behind them so they would know where we were. We would also reach out and touch them on the rump as we walked around them.(Though I wouldn't do that to a horse I didn't know.) It was a good way to let them know things were okay, as you say. We were ALWAYS admonished NOT to walk behind a horse unless they knew we were going to.

Singing to horses reminds me of all the old cowboy tunes used to gentle the herds at night. I reckon the horses liked it, too.