Recently, laser-induced breakdown spectroscopy (LIBS) has been developed for the elemental analysis of geological samples for application to space exploration. There is also interest in using the technique for the analysis of water ice and ice/dust mixtures located at the Mars polar regions. The application is a compact instrument for a lander or rover to the Martian poles to interrogate stratified layers of ice and dusts that contain a record of past geologic history, believed to date back several million years. Here we present results of a study of the use of LIBS for the analysis of water ice and ice/dust mixtures in situ and at short stand-off distances (< 6.5 m) using experimental parameters appropriate for a compact instrument. Characteristics of LIBS spectra of water ice, ice/soil mixtures, element detection limits, and the ability to ablate through ice samples to monitor subsurface dust deposits are discussed.