We performed terahertz time-domain spectroscopy for methylammonium (MA) lead halide perovskite single crystals and characterized the longitudinal optical (LO) phonons directly. We found that the effective LO phonon wave number does not change in the wide temperature range between 10 and 300 K. However, the coupling between MA cation modes and the LO phonon mode derived from lead halide cages induces a mode splitting at low temperatures and a damping of the LO phonon mode at high temperatures. These results influence the interpretation of electron-LO phonon interactions in perovskite semiconductors, as well as the interpretations of mobility, carrier diffusion, and polaron formation.