We present a novel experimental tool allowing for kinematically complete studies of break-up processes of laser-cooled atoms. This apparatus, the 'MOTReMi,' is a combination of a magneto-optical trap (MOT) and a reaction microscope (ReMi). Operated in an ion-storage ring, the new setup enables us to study the dynamics in swift ion-atom collisions on an unprecedented level of precision and detail. In the inaugural experiment on collisions with 1.5 MeV/amu O(8+)-Li the pure ionization of the valence electron as well as the ionization-excitation of the lithium target was investigated.