Catalyzes the NAD-dependent oxidation of (R)-2,3-dihydroxypropane-1-sulfonate to (R)-3-sulfolactate. (2R)-3-sulfopropanediol + H2O + 2 NAD(+) = (2R)-3-sulfolactate + 3 H(+) + 2 NADH Binds 1 zinc ion per subunit. Belongs to the histidinol dehydrogenase family. HpsN subfamily.