We present the color-magnitude diagrams and star formation histories (SFHs) of seven ultra-faint dwarf galaxies: Horologium 1, Hydra 2, Phoenix 2, Reticulum 2, Sagittarius 2, Triangulum 2, and Tucana 2, derived from high-precision Hubble Space Telescope photometry. We find that the SFH of each galaxy is consistent with them having created at least 80% of the stellar mass by z ~ 6. For all galaxies, we find quenching times older than 11.5 Gyr ago, compatible with the scenario in which reionization suppresses the star formation of small dark matter halos. However, our analysis also reveals some differences in the SFHs of candidate Magellanic Cloud satellites, i.e., galaxies that are likely satellites of the Large Magellanic Cloud and that entered the Milky Way potential only recently. Indeed, Magellanic satellites show quenching times about 600 Myr more recent with respect to those of other Milky Way satellites, on average, even though the respective timings are still compatible within the errors. This finding is consistent with theoretical models that suggest that satellites' SFHs may depend on their host environment at early times, although we caution that within the error bars all galaxies in our sample are consistent with being quenched at a single epoch. * Based on observations obtained with the NASA/ESA Hubble Space Telescope at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy under NASA Contract NAS 5-26555.