Ian - interesting question, even though I imagine the majority of us will have a hard time identifying even 10 trees of significance, let alone 25. Also, I need to cheat a bit, i.e. I have to speak in terms of "stands of trees" instead of individual trees, since in no case/hole at my home course is an individual tree significant either strategically or aesthetically. So, with bolding for the holes where I believe trees have some meaningful impact/value:
Hole No. 1 - the trees running down the entire right side are functional, i.e. they prevent tee shots from flying onto the driving range and vice-versa, but don't adversely affect the hole strategically speaking.
No. 2 - the trees running down the right side of landing zone are unnecessarily penal, i.e. they mirror and stand along- side a series of artificial mounds, which together serve to make any decent recovery from a fade-slice almost impossible.
No. 3 - the trees running down the left side of this long par 4 (the #1 stroke hole) are functional, preventing hooked tee shots from getting onto the 2nd fairway; but they also hurt the hole playing-wise, since a long drive that is only slightly pulled leaves one more often than not having to simply chip out sideways -- whereas without the trees most golfers would still be left with a long-iron approach into a green that 'opens' from the other side.
No. 4 - a Par 3 over water with no trees in play.
No. 5 - the trees running down the right side of this dog-leg right are functional, protecting the tee boxes for the 4th hole, but also add to the strategy since it is the trees that create the dogleg and beckon you to try to hit a very controlled fade so to have as short an iron as possible into a tricky, upside-down-bowl of a green.
No.6 - a Par 3 over water, with no trees in play.
No. 7 - another longish Par 4, where the trees running on the right side of the landing zone serve a strategic function, i.e. if you play too safely to the widest part of the fairway (and away from the out of bounds and bunkers on the left) you run out of fairway and into the trees -- hampering what would otherwise be a short and easy approach shot.
No. 8 - the only Par 5 on the front side, the trees here serve only the setting, i.e. there are many trees along both sides of the hole, but the fairway is uniformly wide for the entire length of the hole and the trees are all set well back from the lines of play.
No. 9 - the trees on the left side of the landing zone (which is both the preferred side in terms of approaching the green, and the safe side, since the bunkers and mounds and out of bounds/the range are all on the right) serve as on the 7th hole to complicate matters for someone who plays too safe and/or hits it too far.
No. 10 - a Par 5, and like the 8th uniformly wide with the trees all set back from the lines of play, so they are pretty but serve no real strategic function.
No. 11 - a long Par 3, the trees are not in play.
No. 12 - a dogleg right, and I like the trees here. They run along the right side, but (unlike at the 2nd) there is no artificial mounding there and the trees are fairly sparse -- so that, if you try to cut the dog-leg to leave yourself a short approach but fade it too much, you have to deal with the trees, but you still have a chance of hitting the green with a very good shot.
No. 13 - a Par 3 over water, where no trees are in play.
No. 14 - a short Par 4, with trees lining the fairways functionally (i.e. separating the golf holes) and only affecting play on very bad mishits.
No 15 - a long Par 3, with no trees in play.
No. 16 -- a dog-leg right Par 5, with the trees that function on the right-side of the 12th hole serving the same function here, and fairly well, i.e. cutting too much of the dog-leg leaves a difficult but far from impossible second shot.
No. 17 - a short, sharply dog-legging Par 4, with trees at the far end of the landing zone (if you play a straight and safe shot) affecting your approach if you've played too safe or hit it too far; in other words, the trees here function sort of like they do on the 7th hole.
No. 18 - a long dog-leg right Par 4 to an elevated green, with trees on the right side (as on the 1st hole) serving to keep errant shots out of the driving range and vice-versa, but also (as with the 2nd hole) negatively impacting the hole because there is also artificial mounding there, so a fade that fades too much leaves little chance for anything more than chipping out sideways.
Well, there you have it, Ian. I hope I've given you a decent picture. On my home course (a farmer's field in 1970, with all the trees planted then both to beautify the site and, I assume, to add strategy), there are 6 holes where I believe the stands of trees serve some significant and useful and interesting function.
PS - a couple of asides: 1) in principle I'm neither for nor against trees; some courses may play and look better with significant tree clearing; for others I think it would entail an unnecessary expense (and a short-sighted keeping up with the Jones), 2) my home course, owned by the same family for almost 50 years, is a modestly semi-private/public, and the trees, though there are many, and in some injudicious places, don't seem to affect the agronomics. Indeed, for me the turf and especially the greens are always in wonderful condition -- and a few years ago, after that bad winter, I'm told that the fancy private club up the street 'lost' more than half its greens, while our course got through with barely a scratch.
Peter