Here is a solution that assumes there is one of these .mat files in every subdirectory of each of the 15 directories. Let's also assume that all 15 directories are all in the same directory, and fullrootdirectoryname is its name. Also, there are no other directories in that space. Then you can do the following to visit each directory and load the file:
C = strsplit(genpath(fullrootdirectoryname),':');
startingFolder = pwd;
The business with startingFolder makes sure you end up back where you started, and not in some unexpected place. If any of the above assumptions are not met, this code will need to be modified.