نبذة مختصرة : Antiferromagnetic EuCd$_2$P$_2$ has attracted considerable attention due to its unconventional (magneto)transport properties. At a temperature $T_{\rm peak}$ significantly above the magnetic ordering temperature $T_\textrm{N} = 11\,$K a large peak in resistivity is observed which gets strongly suppressed in magnetic field, resulting in a colossal magnetoresistance (CMR), for which magnetic fluctuations and the formation of ferromagnetic clusters have been proposed as underlying mechanisms. Employing a selection of sensitive probes including fluctuation spectroscopy and third-harmonic resistance, Hall effect, AC susceptibility and $\mu$SR measurements, allows for a direct comparison of electronic and magnetic properties on multiple time scales. We find compelling evidence for the formation and percolation of magnetic polarons, which explains the CMR of the system. Large peaks in the weakly-nonlinear transport and the resistance noise power spectral density at zero magnetic field signify an inhomogeneous, percolating electronic system below $T^\ast \approx 2\,T_\textrm{N}$ with a percolation threshold at $T_{\rm peak}$. In magnetic fields, the onset of large negative MR in the paramagnetic regime occurs at a universal critical magnetization similar to ferromagnetic CMR materials. The size of the magnetic polarons at the percolation threshold is estimated to $\sim 1 - 2\,$nm. The mechanism of magntic cluster formation and percolation in EuCd$_2$P$_2$ appears to be rather robust despite large variations in carrier concentration and likely is relevant for other Eu-based antiferromagnetic CMR systems.
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