IMHO the tightness of your pin will be entirely dependant on the ultimate bearing strength of the wood you're using (which is in the order of 1/10th that of metals and plastics). Essentially you are using a fancy way to drive a nail into the scales without splitting them.

Also, as was said, the runout on your drill is likely more than the thermal contraction you can get on a 1/16" pin in liquid nitrogen.

Cheers,
Dan (B.Eng Building Engineering)