Well, when I go out on Forest Service land I tend to take my own dog to walk point. She likes it. Me too.
And I don’t think that would be a problem here, particularly if you and your dog kept a respectful distance from the herd. These dogs don’t like to leave the herd (can’t protect if you are not with the herd), so they won’t go out of their way to “attack” or pursue you or your dog.