Materials that control ice accumulation are important to aircraft efficiency, highway and powerline maintenance, and building construction. Most current deicing systems include either physical or chemical removal of ice, both energy and resource-intensive. A more desirable approach would be to prevent ice formation rather than to fight its build-up. Much attention has been given recently to freezing of static water droplets resting on supercooled surfaces. Ice accretion, however, begins with the droplet/substrate collision followed by freezing. Here we focus on the behavior of dynamic droplets impacting supercooled nano- and microstructured surfaces. Detailed experimental analysis of the temperature-dependent droplet/surface interaction shows that highly ordered superhydrophobic materials can be designed to remain entirely ice-free down to ca. -25 to -30 °C, due to their ability to repel impacting water before ice nucleation occurs. Ice accumulated below these temperatures can be easily removed. Factors contributing to droplet retraction, pinning and freezing are addressed by combining classical nucleation theory with heat transfer and wetting dynamics, forming the foundation for the development of rationally designed ice-preventive materials. In particular, we emphasize the potential of hydrophobic polymeric coatings bearing closed-cell surface microstructures for their improved mechanical and pressure stability, amenability to facile replication and large-scale fabrication, and opportunities for greater tuning of their material and chemical properties.