Well, my first approach would just be to declare an array of 26 integers (for the letters of the alphabet), then do any tree traversal (preorder, inorder, postorder) that's convenient. At each node, you need a for-loop over the
String; use Character.isLetter() at each char to see if it's a letter. If it is, force it to lower-case, subtract 'a', and increment the integer at that index in the array. Pretty simple.
Now, of course, that's going to work only for ASCII text, and since
Java characters can have many other letter values, there's a large potential for error here. You can deal with this in many ways: ignore it, check each character to see if it's an ASCII letter, use a bigger array (one with 65536 entries)... depends on your problem definition.