Lead-halide perovskites are promising materials in optoelectronic devices for their unique properties including direct band gap, strong light absorption, high carrier mobility, and low fabrication cost. Here, by using ab inito molecular dynamics and electronic structure calculations, we report a systematic study on the broadening density of states (DOS) deep in the valence bands that has been experimentally observed but absent in static calculations. We quantify the broadening DOS reduction from the cubic phase to lower-temperature tetragonal and orthorhombic phases and attribute observed effects to the molecular vibrations and the anharmonicity of iodine atoms motion. Specifically, the MA cations' vibrations are strongly linked to the moderate C-N stretch and CH3 bend, as well as the strong CH3 and NH3+ stretches. These results present a theoretical perspective on the structural dynamics in lead-halide perovskites which may be valuable for future studies toward desired functionalities in perovskite-based optoelectronic devices.