Last year's winner was someone saying the government shouldn't usually be managing common-pool resources like water or land, that in most case private management or polycentric management by the people themselves over the commons is preferable.
Is she an Austrian? Not really. She made some of the same arguments though and reaches the same conclusions as most of them. Austrians are writing books about her work, and embracing it, for what that's worth.
http://www.amazon.com/Challenging-Institutional-Analysis-Development-Bloomington/dp/0415778212/
Out the prizes, arguably eleven people have won (Hayek, Stigler, Coase, North, Freidman, Williamson, Ostrom, Kahneman, Tversky, Smith, Buchanan) who have a detectable or blatant Austrian/NIE/Behavioral approach and conclusions.
(EDIT: Added Stigler and Friedman, because they really are pretty "free-market" even though their approaches fall outside of the common Austrian/behavorial methodology)