Tetrataenite is a promising candidate for rare earth-free permanent magnets due to its low cost and intrinsic magnetic properties. This work investigates the effect of combined milling at liquid nitrogen temperatures (cryomilling) and the addition of carbon as an interstitial element for promoting the formation of tetrataenite. Crystal structure, microstructure, and magnetic properties are investigated to understand the influence of mechanical processing and compositional modifications. No unambiguous evidence of the ordered phase of tetrataenite is found in the structural characterization. However, using Scanning Transmission Electron Microscopy (STEM) and powder X-ray diffraction (PXD) analyses, the occurrence of both twinning and stacking faults resulting from the high-energy milling process is observed, which is a relevant factor for identifying tetrataenite in FeNi alloys. The probability of a stacking fault and twinning occurring for a carbon-free FeNi sample before annealing is found to be 2% and 1.4%, respectively. After annealing, the stacking fault probability decreased to 1.2%, while that of twinning was 1.4%. By increasing the carbon concentration to 5 at.%, the stacking faults and twinning probabilities decrease slightly to 1.2% and 1.3%, respectively. The occurrence of stacking faults combined with small crystallite sizes was a hindering factor in identifying the presence of tetrataenite.