I agree with David in the use of the word "redundant" trees on the Lake. And Evan, I agree that having a decision to make on whether to fade or hook a shot around is fair game except, on #4 and #5, as you suggests, if you miss your tee shot right, you lose the ability to make that decision as there is a forest of trees.
I think a distinction can be made as to having "trees" versus having a "forest of trees". There are many spots where the redundant trees make a forest that is unnecessary for the challenge of strategy and play. The trees on the left of #5, the elbow in the dogleg, they only impact your tee shot if you badly hook one off the tee and they have little purpose for playing #12. If those trees were not there, you would get a nice little breeze coming down the hill, that would effect the flight of the second shot on #12 and possibly the tee shot on #13.
If many of the trees were not there, the wind would have a greater impact on the Lake. No better example of this then on #1 where the trees on the left buffer the wind until you hit your short iron third shot. Many first time players are surprised by the movement of their ball on that shot.
I also am not advocating cutting down any trees, although the conintued thinning of branches will bring back the ability to work the ball out of trouble. Mother nature has its own tree removal program.
Did I mention Euchalyptus? All of those can be removed, they are not native, they are dirty ...