Recent studies on torque vectoring control for electric vehicles proposed various efficient solutions demonstrating improvement of vehicle stability for evasive manoeuvres. However, the torque vectoring on very low friction surfaces such as black ice or wet snow is rarely investigated, especially for the electric vehicles with off-road capability. The presented study contributes to this topic by laying the groundwork for further advanced torque vectoring designs. Within the framework of this paper, the target vehicle is a sport utility vehicle equipped with four on-board electric motors controlling each wheel separately. The functionality of the developed controllers is tested under hardware in the loop simulations for icy road conditions. For this purpose, the tyre model has been parameterized and validated based on the experimental data conducted on a unique terramechanics test rig at Virginia Polytechnic Institute and State University. The test results confirm very good functionality of the developed controllers and demonstrate an improvement of the electric vehicle driving performance.