The behavior of low concentrations of methanol (0.5 and 1.0 wt% of water) as a promoter for hydrate formation in seawater or pure water metastable solutions of methane was investigated using the classical molecular dynamics method at moderate temperature and pressure. The influence of methanol on the dynamics of the re-arrangement of the hydrogen bond network in seawater and pure water solutions of methane was studied by calculating order parameters of the tetrahedral environment and intermolecular torsion angles for water molecules, as well as by calculating the number of hydrogen bonds, hydrate, and hydrate-like cavities. It was found that hydrate nucleation can be considered a collective process in which the rate of hydrate growth is faster in systems with low concentrations of methanol, and confident hydrate growth begins earlier in a metastable solution without sea salt with a small amount of methanol than in systems without methanol.