Mössbauer spectroscopy (MS) measurements were conducted on ammonium iron formate, [NH₄][Fe(HCOO)₃] (AFeF), and dimethylammonium iron formate, [(CH₃)₂NH₂][Fe(HCOO)₃] (DMAFeF), under non-ambient conditions. The electric ordering of the NH₄⁺ and DMA cations is correlated with changes in the local iron environment, which could have implications for the magnetoelectric coupling. In particular, MS was collected upon cooling to 5 K, upon compression up to 10 GPa, and upon both cooling and compression. In the case of AFeF, the ferroelectric ordering upon cooling showed no change in the hyperfine parameters of the iron site, suggesting that no multiferroic coupling would be expected in the magnetic state. Upon compression, two distinct iron sites are observed that could arise from the symmetry-lowering transitions, yielding two symmetry-independent Fe sites. For DMAFeF, the electric ordering of the DMA cation observed upon cooling and upon compression had an impact on the local iron coordination environments. This observation is in agreement with the multiferroic properties observed for this compound. The low-temperature crystal structure of DMAFeF was measured in order to compare with the MS measurements and revealed a static disorder of the DMA cations in the ferroelectric phase, giving rise to at least two distinct iron sites in the Mössbauer spectrum. Upon further cooling below 15 K, the magnetic order of DMAFeF displayed a complex Mössbauer spectrum with at least three iron sites, which could be linked to the number of hydrogen bonds each iron center experiences. The effect of pressure on the magnetic exchanges at low temperature was also studied and revealed an enhancement for DMAFeF at 1.6 GPa, as indicated by the increased internal magnetic fields.