  We use resonant elastic x-ray scattering to determine the evolution of
magnetic order in EuCd$_2$As$_2$ below $T_\textrm{N}=9.5$\,K, as a function of
temperature and applied magnetic field. We find an A-type
antiferromagneticstructure with in-plane magnetic moments, and observe dramatic
magnetoresistive effects associated with field-induced changes in the magnetic
structure and domain populations. Our \textit{ab initio} electronic structure
calculations indicate that the Dirac dispersion found in the nonmagnetic Dirac
semimetal Cd$_3$As$_2$ is also present in EuCd$_2$As$_2$, but is gapped for $T
< T_\textrm{N}$ due to the breaking of $C_3$ symmetry by the magnetic
structure.
