Brian,
It's hard to put one blanket, one system, over an entire approach to individual trees.
But I would mention these criteria in gross:
The "Gotta Go" Factors
AIR+LIGHT = if a tree (or small copse of them) is creating turf issues in areas of regular play, it's got to go.
RECOVERY = if a tree is shutting down or limiting a recovery (or heroic) avenue for a ball out of position on a hole, it's got to go.
EXISTING HAZARD = if a tree is in the line of play (frequent or not) for where a hazard "drop" occurs, it's got to go.
TEE CORRIDOR = Here I'm NOT referencing the tree at or near the landing zone, but the 200-225 yard corridor along the way. If a tree (or small group of them) regular interfere with the ability of a shot to reach the landing zone, it's got to go.
For me Brian, these are the absolute no-brainers, things I could advise from a chair in CT, without ever seeing the course.
The next list, really bears individual site examination, informed by both the maintenance side and the people who have the most voluminous experience of how the course plays and exists for recreation, championship purposes, etc.
A. SHADE -
B. LANDMARK - as an aiming spot and/or yardage token for blind, semi-blind or doglegging holes/shots.
C. HISTORICAL STRATEGIC VALUE - has a particular tree continually played an historical/intended part in the conduct of a hole? Though it may be arbitrary and capricious in that effect, perhaps that bit of fortune is desired and just for THAT hole.
D. QUALITY of SPECIMEN IN QUESTION
E. BARRIER for SOUND and/or NEIGHBORHOOD
F. SAFETY - sometimes this is overstated by some who want a tree to stay and undervalued by some who want it gone, this is why no objective standard can be applied from afar for all trees. Someone like a a long-time caddie or senior player who's seen perhaps thousands of rounds on a hole is usually best qualified to say what tree is or isn't a safety barrier.
Lastly, there is the rare instances when a tree (usually) a group is
**a "SAVER" and not a "DESTROYER" - sometimes a tree's removal can remove a helpful guardian, one that keeps balls from OB or water or just frequents its ricochets back into play. This is a rare case, but I mention it because one of the courses I work at has two holes (or trees on them) where the removal of a certain tree would be a bad thing as it is usually aiding the errant ball back in to a better place.
So Brian I guess my final summary is that there are a handful of absolute factors for evaluating a tree from afar and another handful that are specific to the provincial experience.
Should factors from either list contradict however, I think the list of absolute factors should hold sway.
cheers
vk