Mike,
If you’re serious about this, here’s what I’d do. Find a current long-time member who is a very good player, and is older and highly respected. Walk the course with him, and show him specific trees that you believe have compromised the architectural integrity of the course, and discuss why you feel that way. Then let him take that up with the head pro/GM and the Superintendent; those are the people that will ultimately make the call on tree cutting.
I think it’s important that you talk about a very few SPECIFIC trees, as opposed to just saying, “The trees have gotten bigger and a lot of them need to be cut.” Two obvious examples would be trees that have grown up in line between a fairway bunker and the green so that recovery from the bunker becomes impossible, and trees that have filled out to the extent that they take away options off the tee and require everyone to hit the exact same shot. Both of these are very common on older courses, as I’m sure you already know. Also, you might include turf health in the discussion, which might get the Super more interested.
Good luck with this. I’ve seen it done, but the level of member resistance to tree cutting can be pretty intense. You have a chance, though, if you’re talking about 3 or 4 trees that members are hitting routinely.