By just taking a walk through the woods, or looking up from the ground you can easily tell if a tree is old enough to be cut down. This comes with a number of factors, some that are obvious to the experienced hiker and others that are not as easy to notice at first.
Wide, flat leaves on the top of the tree and narrow, long, low leaves on the sides is a clear sign that the tree is large and has been cut down for a number of years. These characteristics mean that the tree was able to reach a certain height and length before the trees large leaves spread out. Long branches extending out of the trunk and over the edges of the canopy leaves indicate that the tree is big enough to support these branches and roots so they are left untouched.
Wider leaves are a tell tale sign that the tree is old and needs to be cut down, but it can take some work to find the telltale signs of mature cottonwood trees. When it comes to tree cutting, nothing works better than a bird's eye view of the entire tree and this is usually best achieved by using binoculars. Take note of the tips or points where the largest leaves extend from the trunk and the bottoms of the leaves are spread out; these are the areas where the tree has been cut down.
Wide, long, narrow leaves at the same height and spread out are a clear sign that the tree is in a mature condition and ready to be cut down. Mature cottonwood trees will have wide, wide leaves and a wide spread of those leaves in the process of growth. One thing to remember when using binoculars is that they can only make out a specific area that they can see from their vantage point; the area that you are able to see is not necessarily the entire tree. Try to avoid judging trees using binoculars as a rule as they will likely give you an inaccurate picture.
Wide and spreading leaves indicate that the tree is old and being cut down; when trying to find signs of old growth a narrower angle should be used. Once you have found a wide spread of leaves on the tree you can use binoculars to focus on the tops of those leaves, see if the leaves are white or black, depending on whether or not there is a hole in the top.
Wide, narrow leaves on the trunk is a sure sign that the tree is mature, older, and is in a pruning cycle. If this is the case you will be able to locate the center of the trunk and locate the pruning holes by looking at these holes.
Wider, lower branches on the tree indicates that the tree is young and is still growing, if the tree appears to be wide, wide and spreading leaves or buds you will need to be careful. If the tree is old, you will be able to find the top of the tree with your binoculars and determine if it is a mature tree or just a branch that is starting to grow. The tree may appear large to you but your binoculars cannot measure it to the same degree as a person can, this is why you need to be able to observe a tree's branches.
Wide, narrow leaves are a tell tale sign that the tree is young and could still be growing. Using binoculars to observe is your best bet to determining the age of the tree. For some more information on trees see here.