  We use deep Gemini/GMOS-S $g,r$ photometry to study the stellar populations of the recently discovered Milky Way satellite candidates Horologium I, Pictor I, Grus I, and Phoenix II. Horologium I is most likely an ultra-faint dwarf galaxy at $D_\odot = 68\pm3$ kpc, with $r_h = 23^{+4}_{-3}$pc and $\langle $[Fe/H]$ \rangle = -2.40^{+0.10}_{-0.35}$\,dex. It's color-magnitude diagram shows evidence of a split sub-giant branch similar to that seen in some globular clusters. Additionally, Gaia DR2 data suggests it is, or was, a member of the Magellanic Cloud group. Pictor I with its compact size ($r_h = 12.9^{+0.3}_{-0.2}$pc) and metal-poor stellar population ($\langle $[Fe/H]$ \rangle = -2.28^{+0.30}_{-0.25}$) closely resembles confirmed star clusters. Grus I lacks a well-defined centre, but has two stellar concentrations within the reported half-light radius ($r_h = 1.77^{+0.85}_{-0.39}$ arcmin) and has a mean metallicity of $\langle $[Fe/H]$ \rangle = -2.5\pm0.3$. Phoenix II has a half-light radius of $r_h = 12.6\pm2.5$pc and an $\langle $[Fe/H]$ \rangle = -2.10^{+0.25}_{-0.20}$ and exhibits S-shaped tidal arms extending from its compact core. Great circles through each of these substructures intersect at the Large Magellanic Cloud (LMC). This suggests that these objects are, or once were, satellites of the LMC. 
On the Nature of Ultra-faint Dwarf Galaxy Candidates. III. Horologium I,   Pictor I, Grus I, and Phoenix II