Finite element exterior calculus (FEEC) is a framework that allows for results proved on general differential complexes to be applied to a large class of mixed finite element problems. In earlier work, using this framework, we introduced a convergence and optimality result for a class of adaptive mixed finite element problems posed on polygonal domains. In this talk we discuss the extension of these results to problems on Euclidean hypersurfaces. More specifically, we introduce a method and prove rates of convergence for problems posed on surfaces implicitly represented by level-sets of smooth functions.