The exploration of ice sheets by melting vertical holes into the ground has some tradition in terrestrial glaciology. Such probes have been used since the 1960's to investigate the vertical structure of the ice in Greenland and Antarctica and in alpine glaciers. In this paper we look into the possibility to develop similar devices for use on extraterrestrial icy bodies, like e.g. the polar areas on Mars or the icy satellites of the outer solar system. We report on some basic experiments performed in the cryo-vacuum laboratory of the Space Research Institute of the Austrian Academy of Sciences, Graz. In these experiments the penetration of a simple melting probe into compact and porous water ice (with a snow-like texture) was monitored, both under vacuum conditions and under air pressure. The observed penetration speeds for a given power supply are compared with a simple mathematical model. We conclude that a miniature melting probe with small overall dimensions and a reasonable power demand could well be part of the payload of a future planetary mission, for example to the poles of Mars. Such missions are currently under discussion in several space agencies. Moreover such probes could also e? ectively be used in terrestrial environments. A possible design is presented at the end of the paper.