Annika Sorenstam and Tiger Woods are the most famous exponents of weight training. It's probably just coincidence that when it came out that they were lifting heavy, their games were headed downhill.
Harvey Pennick, or maybe it was Bud Shrake, said that golfers need the kind of muscles that can crack a whip, not lift a wagon, or something like that. That's considered an old fashioned view these days. I'm not so sure.
What do the best golfers in the world look like and how do they exercise? Few to none look like body builders. There are more athletic pro golfers now than in generations past, but they are not muscled like a builder. They are more like past generation football quarterbacks than linemen or running backs. I suspect the strongest guys on tour look heavy and out of shape.
One wonders if some golfers who have been crippled by physical disabilities such as a bad back or painful wrist, could have avoided disability by early weight training. In golf, backs, wrists, shoulders and knees are critical.
Body type. My own speculation is that thick pects and front delts obstruct the golf swing, that sloping shoulders are better than wide straight shoulders, and that it helps to have a long neck and a short chin. That's Tiger Woods btw. Even Tiger Woods the body builder has a rather flat chest. On the other hand, there are some powerfully muscled guys and gals in long drive competition. But they are not playing on the big tour, and more than a few have weird swings.
There are golf specific exercises you can do. I don't know that one should do them a whole lot, because of imbalance and the danger of overuse. Play golf twice a week and do those exercises twice a week and maybe you are overworking certain joints and muscles. There's nothing wrong with a general weight program as long as you are careful, get good advice, and don't lift too heavy or too often. (Careful with flat bench pressing, for example; going heavy there has caused a lot of damage.) I've used weights for 45 years, and it took nearly that long to learn that muscles grow because of a lot of rest and nutrition separated by brief episodes of lifting.