We report on the nature of the low temperature magnetic ordering of a magnetic ionic plastic crystal, Choline[FeCl₄]. This investigation was carried out using heat capacity measurements, neutron diffraction experiments and muon spin relaxation (μSR) spectroscopy. The calorimetric measurements show the onset of an unusual magnetic ordering below 4 K with a possible second magnetic phase transition below 2 K. Low temperature neutron diffraction data reveal a three dimensional antiferromagnetic ordering at 2 K compatible with the previous magnetometry results. The analysis of μSR spectra indicates a magnetic phase transition below 2.2 K. At 1.6 K, the analysis of the shape of the μSR spectra suggests the existence of an additional magnetic phase with features of a possible incommensurate magnetic structure.