We report the development of a handheld, ultra-wideband impulse radar with very low size, weight, and power requirements. This radar is designed to remotely detect different layers in snow or ice that tend to crack or break under certain conditions indicative of potential avalanche hazards. First, the basic hardware design and configuration are introduced. Then, the development of a series of electromagnetics sensing models, which support the training and testing of machine learning algorithms for weak layer detection, is described. The principles and performance of these computational models are compared and validated with lab and snowpack measurements. Finally, the machine learning algorithms are applied to different snow profile measurements to generate hardness profiles for the user.