Controlling anisotropy in self-assembled structures enables engineering of materials with highly directional response. Here, we harness the anisotropic growth of ice walls in a thermal gradient to assemble an anisotropic refractory metal structure, which is then infiltrated with Cu to make a composite. Using experiments and simulations, we demonstrate on the specific example of tungsten-copper composites the effect of anisotropy on the electrical and mechanical properties. The measured strength and resistivity are compared to isotropic tungsten-copper composites fabricated by standard powder metallurgical methods. Our results have the potential to fuel the development of more efficient materials, used in electrical power grids and solar-thermal energy conversion systems. The method presented here can be used with a variety of refractory metals and ceramics, which fosters the opportunity to design and functionalize a vast class of new anisotropic load-bearing hybrid metal composites with highly directional properties.