Tree management is exactly what it implies, management.
I cannot tell you how many holes on Ross designed courses have been abased over the years by the willy-nilly planting of trees for the sake of separating the holes (ala Pine Valley). Avenues have been cut off, strategy has been changed and the agronomics have been compromised.
Many times repeated plantings have turned wonderful straight forward golf holes into untoward badly angled dog legs. I have seen fairways that have been moved as many as 60 yards by the tree additions of the 30's, 40's, 50's, 60's, etc.
Another problem is that trees have often compromised the fairway bunkering on golf courses. Some well intentioned soul plants a seedling 20 yards in front of a fairway bunker only to create a double hazard within ten years. Too many times I have seen the bunker removed in an effort to save the latter day tree.
Management is what is necessary. Trees that surround the perimeter of the course are often quite attractive and have no negative impact on the course. Trees surrounding the back of a green usually causes an agronomic nightmare. Many times I have pointed out the outline of the canopies of the surrounding trees on the surface of the green.
Balance is necessary and can only be reached through proper management.
Oakmont is a very special place. The ground was nearly treeless in 1903 when the course was built. The course has all the difficullty and hazard one can deal with without having to face vertical hazards. To be able to stand on the eighteenth tee and see most of the course is really pretty cool.
The tree removal at places like Aronimink, Salem, Beverly, Minkahda, Pine Needles, Pinhurst #2 and many others has vasly improved these courses from both an agronomic and golf point of view.
The planting of trees at Augusta is an anomoly. Augusta is attempting to control the scoring in a major Championship.
They will do what they feel is necessary.
The average Country Club must look to it's origins, the avenues of play and the original angles of intent of the Architect before they make any tree decisions. After this assessment I feel that most clubs will opt for removal rather than addition.