Neil,
I am the current Green Chairman at Tavistock CC (Haddonfield NJ). We undertook a long term tree management program about 7 years ago. Although I wasn't chair at the time it started, I was involved with getting it off the ground and sold to the membership.
We first started the process during our planning for our Restoration Master Plan and put it together with our architect Jim Nagle as well as with Dave Oatis from the USGA Green Section.
Our course is a classic Philadelphia area parkland course that had been grossly overplanted with White Pines and other types during the 1960-70's. We put together a comprehensive report and plan and really tried to educate our membership on the merits of such a program. We have completed a large majority of the work but still have more to finish. Although we still get the occasional bitching from a certain segment of golfers, by and large, the program as been well received. Our course is in the best condition as it has ever been, we've opened up some beautiful vistas throughout the course and the overall playability is much better.
The common complaint we always got was that we were making the course too easy and you'll come to realize that's just a very silly comment made by uneducated members in regard to tree removal. The average club member is simply not good enough to have any real scoring difference even with a more open design. It might be slightly easier for the better players but even then, that's not always the case. The scoring during our Club Championship qualifying rounds this year was the highest I can remember and we have less trees on the course then we had 50 years ago.
As a final tip, I think it is extremely beneficial to have a consulting architect or someone like Dave Oatis come in and speak to the entire membership about this issue. It adds another level of credit to the Green Chair/Committee in selling such a program and goes along way in the education process of the members.
Good luck