Ice accumulation hinders the performance of, and poses safety threats for, infrastructure both on the ground and in the air. Previously, rationally designed superhydrophobic surfaces have demonstrated some potential as a passive means to mitigate ice accretion; however, further studies on material solutions that reduce impalement and the contact time for impacting supercooled droplets (high viscosity) and can also repel droplets that freeze during surface contact are urgently needed. Here we demonstrate the collaborative effect of substrate flexibility and surface micro/nanotexture on enhancing both icephobicity and the repellency of viscous droplets (typical of supercooled water). We first investigate the influence of increased viscosity (spanning from 0.9 to 1078 mPa.s using water glycerol mixtures) on impalement resistance and the droplet substrate contact time after impact. Then we examine the effect of droplet partial solidification on recoil and simulate more challenging icing conditions by impacting supercooled water droplets (down to 15 degrees C) onto flexible and rigid surfaces containing ice nucleation promoters (AgI). We demonstrate a passive mechanism for shedding partially solidified (recalescent) droplets under conditions where partial solidification occurs much faster than the natural droplet oscillation which does not rely on converting droplet surface energy into kinetic energy (classic recoil mechanism). Using an energy-based model (kinetic elastic capillary), we identify a previously unexplored mechanism whereby the substrate oscillation and velocity govern the rebound process, with low areal density and moderately stiff substrates acting to efficiently absorb the incoming droplet kinetic energy and rectify it back, allowing droplets to overcome adhesion and gravitational forces, and recoil. This mechanism applies for a range of droplet viscosities, spanning from low-to high-viscosity fluids and even ice slurries, which do not rebound from rigid superhydrophobic substrates. For a low viscosity fluid, i.e., water, if the substrate oscillates faster than the droplet spreading and retraction, the action of the substrate is decoupled from the droplet oscillation, resulting in a reduction in the droplet substrate contact time.