Mayday,
Though the trees appear healthy, they are not. In the natural environment, a thick forest of trees and thick stand of turf do not occur together. Granted, trees occur naturally in a grass land environment, but the dominant species is the grass not the trees. One always dominates the other, they cannot thrive together.
Trees on a golf course are not healthy because the abundant water and nutrients cause the tree to grow thin and weak with shallow roots. Easily toppled over in a strong wind or heavy snow. In the natural environment, trees grow slow with deep roots looking for water. At least here in the high desert of central Oregon. On the other side of the mountains (Portland), the trees are shallow rooted and fast growing. If some topple over, there are hundreds more to take its place.
Trees on a golf course should be, IMHO, slow growers, easily adapted to shallow water supplies, and used as accents to the layout but not dominant. Trees should be planted in odd numbers to look more natural occurring, groups of three, five, seven...
How many golf courses have you played that have tall weak-wooded poplar trees planted with the thought that the 80% air mass of the tree will "protect" golfers from being hit by balls? These trees litter the golf course when ever a strong wind blows through with branches and leaves. Willows do the same. Plant these trees out of play if they must be planted.
All in all, golf courses are not the best place for trees, whether because of their poor health, poor siting, and/or poor selection of species.
Troy