The quantum solid para-hydrogen (p-H2) has recently proven useful in matrix isolation spectroscopy. Spectral lines of compounds embedded in this host are unusually narrow, and several species have been reported to rotate in p-H2. We found that a p-H2 matrix inhibits rotation of isolated methanol (CH3OH) but still allows internal rotation about the C-O bond, with splittings of the E/A torsional doublet in internal rotation-coupled vibrational modes that are qualitatively consistent with those for CH3OH in the gaseous phase. This simplified high-resolution spectrum further revealed the slow conversion of nuclear spin symmetry from species E to species A in the host matrix, offering potential insight into nuclear spin conversion in astrophysical sources.