A lot of times I think that people wear their "busyness" as a badge of honor. They feel that if every minute of every day is filled with something, then they are somehow better off or better than a person that is less busy. Thoreau's emphasis on "simplicity, simplicity, and simplicity" is largely missing from daily modern life I believe.
Santiago's sheep enhance his life and allow him to live happier, because they offer simplicity. I don't believe that being a shepherd is easy, but the sheep for the most part are predictable and do what he wants them to do. He knows what to expect from them, and he has a great deal of control over them. Santiago isn't even necessarily bored by them, because he admits that he "usually learns more from sheep than from books." The sheep offer Santiago a happy life because they offer a simple, content life.
Of course Santiago eventually grows restless and wants to leave the life of a shepherd in order to pursue his personal legend. He goes on a fantastic adventure, but it is fraught with danger. Santiago frequently debates giving up and just going back to the life he knows and the life that he knows allowed him to be content. The sheep might not be glamorous like a personal legend, but I could argue that being content is equivalent to being happy.