A better answer for Noel now that I'm home with my books. Straight from the horse's mouth:
"Despite the early and continuous enthusiasm with which the game was played in Scotland, many chroniclers have tried to prove that golf originated on the Continent. There is not the slightest scintilla of evidence to support this. Numberless games with club and ball have been played for the past two thousand years, and doubless for millenniums before; but no game with more than one club and with a separate ball for each plyer, and no game having as its goal a designated hole in the ground. Caesar came as close as any to modern golf when he played Paganica to a mark-- but not to a small hole in the ground -- with one club and the sort of leather ball stuffed with feathers which Scotchmen used before the discovery of the gutta percha.
"There are many other Continental rivals to golf. There is even a resemblance of name in the German word Kolbe and the Dutch word Kolf, each signifying 'club.' And Dutch pictures and tiles of the sixteenth and seventeenth centuries show men playing a game which has a superficial resemblance to the Scotch sport so far as the club goes. Actually it resembles golf in no other particular. It is nearly always pictured as a winter game on the ice, with the goal as a post. Later kolf came indoors and was played in a rectangular space sixty by twenty-five feet with a floor as hard and level as a billiard table enclosed by walls two feet high, from wich the ball could be made to rebound accurately against posts placed near either end. The French game of jeu de mail comes closer to golf, being played cross-country, with a kind of croquet mallet and to posts or raised marks.
"Why so many historians of the the game have so persistently interpreted kolf as golf I fail to comprehend. As Andrew Lang says in 'Badminton': 'Clearly golf is no more kolf than cricket is poker.' The only explanations I can see lies in the facility with which Dutch painters turned out pictures of their countrymen playing with kolf club and ball. In the golf collection which I purchased from Doctor W. Laidlaw Purves, a noted Scotch golfer who founded the Royal St. George's Golf Club of Sandwich, there are some twenty pictures of Dutch kolf scenes from paintings and many Delft tiles including one from which the little figures used as insignia of the National Golf Links of America and the Links Golf Club near New York were taken. All of these Doctor Purves collected during some years of residence in Holland, but not one represents a true golfing scene. Yet they can and do lead astray the golf enthusiast who seeks some concrete evidence of the origin of his favorite sport."
-Charles Blair Macdonald, Scotland's Gift: Golf, pp.8-12.