Differential cross sections and complete sets of polarization observables are presented for the Gamow-Teller $^{12}{rm C}(vec{p},vec{n})^{12}{rm N}({rm g.s.},1^+)$ reaction at a bombarding energy of 296 MeV with momentum transfers $q$ of 0.1 to $2.2{rm fm}^{-1}$. The polarization transfer observables are used to deduce the spin-longitudinal cross section, $ID_q$, and spin-transverse cross sections, $ID_p$ and $ID_n$. The data are compared with calculations based on the distorted wave impulse approximation (DWIA) using shell-model wave functions. Significant differences between the experimental and theoretical results are observed for all three spin-dependent $ID_i$ at momentum transfers of $q gtrsim 0.5{rm fm}^{-1}$, suggesting the existence of nuclear correlations beyond the shell model. We also performed DWIA calculations employing random phase approximation (RPA) response functions and found that the observed discrepancy is partly resolved by the pionic and rho-mesonic correlation effects.