I tend to do this as well, I find breathing, especially while trotting kinda hurts because of the choppiness sometimes. I also do it out of nerves, especially if I haven't ridden in a while.
You stop breathing and then your whole body tenses and then the horse can feel the tension, which in turn will make the horse uncomfortable as she is getting mixed signals from you, the rider.
I like having music to listen to or have someone to talk to. Sometimes I even carry on conversations with the horse (sometimes passerbys look at me like I'm crazy
). I haven't tried singing though.