There are different methods of fast hydrogen generation by reaction of metal powder with water. Fundamental study of combustion of aluminum-water compositions with frozen water (aluminum-ice [ALICE]) is of great interest for the rocket technique applications. New solid hydro-reactive compositions of ALICE type on the base of permeable micro-porous metal-polymer matrices filled with water is reported. Magnesium (Mg) powder of 80m was chosen as a combustible. Combustion characteristics for these compositions in a nitrogen or argon atmosphere at different pressures were studied. It was found that the burning rate was 12-18mm/s in the wide pressure range up to 80atm, as the pressure exponent was close to zero. It was shown that the presence of a thin agglutinant polymer film on the Mg particle of the metal-polymer matrix did not significantly affect the burning rate of samples in comparison with mixtures of Mg powder with water but resulted in some combustion peculiarities. Preliminary experiments studying the combustion wave propagation along the metal-polymer matrix surface in water steam were carried out.