Thin film ferromagnet/antiferromagnet (F/AF) exchange biased structures that are widely used in GMR spin valves are considered nowadays as promising systems for antiferromagnetic spintronic and spin-orbitronic devices. Here, the temperature dependences of magnetization dynamics in Co/IrMn and Co/FeMn F/AF structures are investigated using ferromagnetic resonance (FMR) in comparison to a free Co layer. A strong additional decrease in the resonance field was observed in Co/IrMn with a temperature decrease attributed to the rotatable anisotropy increase, which almost vanished at room temperature. In contrast to Co/IrMn, the contribution of the rotatable anisotropy in Co/FeMn is much weaker, even though it exists at RT, it is negative, and slightly varies with the temperature and resonance field shift in Co/FeMn. This is mainly due to unidirectional exchange anisotropy. FMR linewidth for the free Co layer increases with decreasing temperature and is accompanied with a slow relaxation process, while the additional contribution to FMR line broadening in Co/IrMn and Co/FeMn structures is correlated with variation in the exchange anisotropy. The observed results are discussed based on structural and surface morphology and magnetization reversal characterization using X-ray diffraction, atomic force microscopy, and vibrating sample magnetometry data.