We present a suite of high-resolution numerical simulations to study the evolution and survival of dust in hot galactic winds. We implement a novel dust framework in the Cholla hydrodynamics code and use wind tunnel simulations of cool, dusty clouds to understand how thermal sputtering affects the dust content of galactic winds. Our simulations illustrate how various regimes of cloud evolution impact dust survival, dependent on cloud size, wind properties, and dust grain size. We find that significant amounts of dust can survive in winds in all scenarios, even without shielding from the cool phase of outflows. We present an analytic framework that explains this result, along with an analysis of the impact of cloud evolution on the total fraction of dust survival. Using these results, we estimate that 60% of 0.1 μm dust that enters a starburst-driven wind could survive to populate both the hot and cool phases of the halo, based on a simulated distribution of cloud properties. We also investigate how these conclusions depend on grain size, exploring grains from 0.1 μm to 10 Å. Under most circumstances, grains smaller than 0.01 μm cannot withstand hot-phase exposure, suggesting that the small grains observed in the circumgalactic medium (CGM) are either formed in situ due to the shattering of larger grains, or must be carried there in the cool phase of outflows. Finally, we show that the dust-to-gas ratio of clouds declines as a function of distance from the galaxy due to cloud–wind mixing and condensation. These results provide an explanation for the vast amounts of dust observed in the CGMs of galaxies and beyond.