Precise knowledge of the dielectric properties of natural snow, firn and ice are essential for electromagnetic remote sensing of the cryosphere. In glaciological applications, the vertical distribution of dielectric properties can be obtained from ice core measurements by means of dielectric profiling (DEP), nowadays routinely used in polar drillings. Dielectric profiles allow to link ice core properties with coherent reflections seen in ground-penetrating radar (GPR) by means of forward modeling GPR signals. However, as DEP operates at a few 100 kHz, the results have to be transferred to radio frequencies in the MHz-range. Here we investigate the dielectric properties of ice cores recently drilled at two cold glaciers in the European Alps, Col du Dome, Mont Blanc and Colle Gnifetti, Monte Rosa. Although limited to roughly 100 m in thickness, these glaciers comprise strong gradients in ice characteristics, such as impurity content and crystal orientation fabric, as well as a comparatively large depth-fraction of firn. We applied, for the first time, DEP to these Alpine ice cores. With respect to what is known from polar sites, dielectric profiles at 250 kHz are compared to density, impurity and electrical conductivity measurements. This is to obtain a comprehensive picture on the DEP signals in view of the strong variability in physical properties, and the potential for obtaining DEP-based age information from annual cycles and signatures of volcanic eruptions. Complementary to DEP, we used a coaxial cell setup to measure dielectric properties of selected firn samples directly at radio frequencies from 1 MHz to 1.5 GHz. This combined approach allows us to study the dielectric properties of natural samples over a broad frequency range and to assess the transfer of DEP results to radio frequencies. Finally we include a comparison of forward modeled and measured GPR signals aimed at an improved understanding of englacial reflections at these cold-ice mountain drilling sites.