Oxidizes mannitol to mannose. Provides the initial step by which translocated mannitol is committed to central metabolism and, by regulating mannitol pool size, is important in regulating salt tolerance at the cellular level. D-mannitol + NAD(+) = D-mannose + H(+) + NADH Binds 2 Zn(2+) ions per subunit. Belongs to the zinc-containing alcohol dehydrogenase family.