Three-dimensional lead-halide perovskites have attracted a lot of attention due to their ability to combine solution processing with outstanding optoelectronic properties. Despite their soft ionic nature these materials demonstrate a surprisingly low level of electronic disorder resulting in sharp band edges and narrow distributions of the electronic energies. Understanding how structural and dynamic disorder impacts the optoelectronic properties of these perovskites is important for many applications. Here we combine ultrafast two-dimensional vibrational spectroscopy and molecular dynamics simulations to study the dynamics of the organic methylammonium (MA) cation orientation in a range of pure and mixed trihalide perovskite materials. For pure MAPbX3 (X = I, Br, Cl) perovskite films, we observe that the cation dynamics accelerate with decreasing size of the halide atom. This acceleration is surprising given the expected strengthening of the hydrogen bonds between the MA and the smaller halide anions, but can be explained by the increase in the polarizability with the size of halide. Much slower dynamics, up to partial immobilization of the organic cation, are observed in the mixed MAPb(ClxBr1-x)3 and MAPb(BrxI1-x)3 alloys, which we associate with symmetry breaking within the perovskite unit cell. The observed dynamics are essential for understanding the effects of structural and dynamical disorder in perovskite-based optoelectronic systems.