Catalyzes the NAD(+)-dependent oxidation of L-threonine to 2-amino-3-ketobutyrate. L-threonine + NAD(+) = (2S)-2-amino-3-oxobutanoate + H(+) + NADH Binds 2 Zn(2+) ions per subunit. Amino-acid degradation; L-threonine degradation via oxydo-reductase pathway; glycine from L-threonine: step 1/2. Homotetramer. Belongs to the zinc-containing alcohol dehydrogenase family.