Classical Monte Carlo and molecular dynamics (MD) simulations were carried out to investigate the structures, the infrared spectra, and the rigid-nonrigid transitions of small methanol clusters (CH₃OH)_n, n=3-6. The study was motivated by experimental results for these clusters from size specific infrared (IR) dissociation spectroscopy. The MD simulations revealed the following transitions: The trimer passes from a rigid ring configuration into a series of nonrigid open chain structures starting at 197 K. For n=4 and 5 such transitions occur between rings and rapidly fluctuating ring structures at T=357 and 243 K, respectively. For n=6 first a pure isomeric transition between the two energetically lowest isomers of S₆ and C₂ symmetry is found at 35 K, and then a similar transition to a nonrigid behavior as is observed for n=4 and 5 is seen at 197 K. The measured spectral display in all cases the rigid lowest energy configurations.