  We present new horizontal branch (HB) distance measurements to 17 of the
faintest known M31 satellites ($-6 \lesssim M_{V} \lesssim -13$) based on deep
Hubble Space Telescope (HST) imaging. The color-magnitude diagrams extend
$\sim$1-2 magnitudes below the HB, which provides for well-defined HBs, even
for faint galaxies in which the tip of the red giant branch (TRGB) is sparsely
populated. We determine distances across the sample to an average precision of
4% ($\sim 30$~kpc at $800$~kpc). We find that the majority of these galaxies
are in good agreement, though slightly farther (0.1-0.2 mag) when compared to
recent ground-based TRGB distances. Two galaxies (And~IX and And~XVII) have
discrepant HST and ground-based distances by $\sim 0.3$ mag ($\sim 150$~kpc),
which may be due to contamination from Milky Way foreground stars and/or M31
halo stars in sparsely populated TRGB regions. We use the new distances to
update the luminosities and structural parameters for these 17 M31 satellites.
The new distances do not substantially change the spatial configuration of the
M31 satellite system. We comment on future prospects for precise and accurate
HB distances for faint galaxies in the Local Group and beyond.
