  We study a frustrated dipolar array recently manufactured lithographically by
Wang {\em et al.} [Nature {\bf 439}, 303 (2006)] in order to realize the square
ice model in an artificial structure. We discuss models for thermodynamics and
dynamics of this system. We show that an ice regime can be stabilized by small
changes in the array geometry; a different magnetic state, kagome ice, can
similarly be constructed. At low temperatures, the square ice regime is
terminated by a thermodynamic ordering transition, which can be chosen to be
ferro- or antiferromagnetic. We show that the arrays do not fully equilibrate
experimentally, and identify a likely dynamical bottleneck.
