Ancient theories of mimesis start with Plato, primarily Republic and to a lesser extent Sophist. For Plato, the essential characteristic of both poetry and art is that they are mimetic. Unfortunately, they imitate not the ideal forms, but sensible particulars, which are themselves no more than pale imitations of the forms, and thus art becomes three removes from reality.
Although Aristotle accepts Plato's notion of mimesis as imitation, he is more concerned with its positive values -- that we can learn by imitating good models. While for Plato, the pure mimesis of drama was worse than the mixed mimesis and diegesis of epic, for Aristotle the reverse was true.
Horace follows a generally Aristotelian view of mimesis, but unlike Aristotle was more concerned with how to write literature than its philosophical implications.
Longinus was not as concerned with mimesis as the other three writers, taking a neoplatonic view of art that focussed on how sublime moments could affect the audience.