Many people think since they are racing in the mud they should wear their oldest, worst sneakers. I believe this is a mistake many people will make. Remember, you will be running a considerable distance. It will be muddy and the terrain will be uneven. You will encounter rocks, roots and ruts, and this will demand a good supporting sneaker.
Many off-road runners prefer a good trail sneaker with an aggressive tread instead of a regular running style. Be careful, too much of an aggressive tread and it can fill with mud adding extra weight to carry around.
I suggest a quality sneaker with a medium tread pattern. After the race simply rinse them off with a hose and they'll be as good as new.