Magnetic polarons can generate colossal magnetoresistance in magnetic semiconductors, yet their terahertz electrodynamics remain largely unexplored. Here we report magneto-terahertz spectroscopy of the Eu-based Zintl antiferromagnet EuZn${}_2$P${}_2$. The low-frequency conductivity shows pronounced non-Drude behavior consistent with an evolution from isolated to overlapping magnetic polarons upon cooling. The polaron relaxation time reaches a maximum near the Néel temperature at zero field and exhibits a strong magnetic-field dependence. This polaron-driven reshaping of the conductivity leads to a strongly frequency-dependent magnetoresistance that becomes colossal in the terahertz range, reaching about 90 % at 1.5 THz, roughly three times larger than the zero-frequency limit value. These results demonstrate that magnetic polarons strongly govern the low-energy electrodynamics and highlight the sensitivity of terahertz spectroscopy to polaronic magnetotransport in correlated magnetic semiconductors.