Why is magnesium hydroxide not hygroscopic? I asked this question today and my professor was unable to provide any rationale. 

I know that sodium hydroxide is hygroscopic, but why not magnesium hydroxide (at least to the same extent as $\ce{NaOH}$)? Could it be that $\ce{Mg(OH)2}$ has a higher lattice energy; the hydroxide is more closely associated with the magnesium ion and less able to react with carbon dioxide?
Try looking at Inorganic Chemistry in Aqueous Solution by Jack Barrett around page 41 on google books or elsewhere.  

Entropy of hydration of Mg2+ is very negative compare to Na+.  

According to Barrett, more highly charged ions restrict the movement of water molecules of hydration more.  Also, the smaller the radius of the ion, the more restricted the movement of the hydrating waters is.  Both the number of waters whose movement is restricted, and the degree to which they are restricted, is affected by charge and radius.  

A complete analysis would consider both the entropy and enthalpy contributions.