Polyol dehydrogenase that catalyzes the reversible NAD(+)-dependent oxidation of various sugar alcohols. Is active with xylitol, L-iditol and D-sorbitol (D-glucitol) as substrates, leading to the C2-oxidized products D-xylulose, L-sorbose and D-fructose, respectively (By similarity). Is a key enzyme in the polyol pathway that interconverts glucose and fructose via sorbitol, which constitutes an important alternate route for glucose metabolism (By similarity). NAD(+) + xylitol = D-xylulose + H(+) + NADH L-iditol + NAD(+) = H(+) + keto-L-sorbose + NADH H(+) + keto-D-fructose + NADH = D-sorbitol + NAD(+) Binds 1 zinc ion per subunit. Homotetramer. By cold. Belongs to the zinc-containing alcohol dehydrogenase family.