The intuitive answer is that a healthy, vigorous tree will keep on photosynthesizing late into the fall, while a weak, sick tree will give up and go dormant earlier in the season. In fact, it’s exactly the opposite.
When it comes to the problem of how long leaves should be held onto, a tree faces a dilemma. On the one hand, a tree can only produce food and store energy while it still has its leaves. But on the other hand, as winter creeps closer, having lots of green leaves is a big risk – the leaves could be killed suddenly by a frost, or they could catch flakes in an early snowfall, causing weight to pile up on the tree and increasing the likelihood that branches will break.
In the normal course of things, a tree wants to store all the energy that its leaves have produced, reabsorb the chlorophyll and other useful chemicals from its leaves so they can be used again the following year, and then jettison the leaves and ride out the winter in a dormant state. Ideally, all of this will happen just before frost arrives, thus maximizing photosynthesis and minimizing the risk of frost damage.
Of course, the tree doesn’t know exactly when the first frost will arrive, and so it has to take a bit of a gamble with its timing.
A healthy tree that has stored up plenty of energy for the winter will play it safe, losing its leaves well before cold weather sets in, and relying on its reserves to last until spring. Conversely, a tree that is struggling will run the risk of being injured by a night of freezing temperatures in order to squeeze in a few more days of photosynthesis, in the hopes of storing enough food to make it through to the next growing season.
Thus, trees that settle in for winter early are doing well, and trees that cling to their leaves are desperately trying to survive.