We derive a general semiclassical theory for linear response functions at finite temperatures and finite frequencies for quantum systems with internal ballistic dynamics. As a specific example, we present a detailed quantum mechanical and semiclassical analysis of the infrared absorption in small two-dimensional conducting disks. We incorporate the effect of Coulomb interactions into our semiclassical approach using a Thomas-Fermi approximation, which is valid for low external frequencies. Our semiclassical results are in excellent agreement with corresponding quantum calculations.