Catalyzes the NAD-dependent reversible oxidation of D-threitol. Involved in the degradation pathway of D-threitol, that allows M.smegmatis to grow on this compound as the sole carbon source. Does not catalyze the oxidation of xylitol, L-sorbitol, and L-sorbose. D-threitol + NAD(+) = D-erythrulose + H(+) + NADH kcat is 6.97 sec(-1) with D-threitol as substrate. kcat is 0.71 sec(-1) with D-threose as substrate. kcat is 7.32 sec(-1) with D-erythrulose as substrate. Carbohydrate metabolism; D-threitol degradation. Up-regulated during growth on D-threitol relative to growth on glycerol. Complete loss of the ability to grow on D-threitol. Belongs to the short-chain dehydrogenases/reductases (SDR) family.