We ride with dogs, and it does seem to calm the horses. They seem to look to the dogs we take as partners who would warn them of danger, and get nervous if they can't find the dogs. Our dogs learn not to stand in front of the horse, or nip at them, or they get kicked, so we've never had too much of a problem in that department.
The one thing I didn't like is we used to have a rat terrier who did the trails with us. Hoover hated that dog, and was never calm when she was around. Bigger dogs, like our lab and collie mixes, he's fine. He seems to get they look out for him. Smaller dogs, he would kill if he got the chance.
"Sit tall in the saddle, hold your head up high. Keep your eyes fixed where the trail meets the sky. And live like you ain't afraid to die...don't be scared, jut enjoy the ride." - Chris LeDoux