Catalyzes the NAD(H)-dependent interconversion of D-fructose and D-mannitol in the mannitol metabolic pathway. D-mannitol + NAD(+) = D-fructose + H(+) + NADH There are two genes for this mannitol dehydrogenase in yeast, DSF1 and YNR073C. Belongs to the mannitol dehydrogenase family.