Some interesting replies to this thread so far.
We have an 11-month old pup, named "Seve", that we picked up last spring at 8 weeks old. He is a hunting breed (pointer), and has had an incredible amount of energy since we first brought him home, therefore requiring multiple daily walks, training, playtime, etc. When he was only about 10 weeks old or so, I would bring him out my home course at sunrise well before the greens crew was even out prepping the course for short walks, on a lead, in the name of exposure to different environments. He went off to be trained to hunt upland birds this past summer/fall from late July to early October and can now be handled pretty easily with the aid of an 'e-collar' which I rarely need to use outside of a vibrate to get him to recall if he's getting out a bit too far. Since the golf course closed in early November, every day that I am home with daylight I take my pup to the golf course to run as we live exactly one city block away from the eastern border of the course. He absolutely loves it. He gets to put his "afterburners" on running around the course and typically points, sometimes brings me back some sort of animal (moles, dead crows, rabbits, etc.), and he gets to meet and run around with some of the other dogs that are out on the course.
I had been prepared to take my pup out for early summer morning runs on the course this upcoming season...but after reading Ian's posts and related links I'm second guessing myself now.
I personally love the idea of playing a round of golf with a dog, and I love the set ups at places like Swinley Forest or even Sutton Bay here in the US where you can let your dog run while you play. But I'm a "dog guy" and I understand that not everyone is. Not to mention that the vast majority of dogs, in particular here in the US, are not properly trained and I wouldn't want running around a course full of golfers. I suppose it's like anything else...use your common sense...but then sometimes that is lacking in this world