Polarimetric synthetic aperture radar is expected to distinguish wet snow from bare ground. However, since both of them show surface scattering, which is sensitive to incidence angle, it often fails in the distinction in mountainous areas. In this letter, we propose an adaptive distinction method using quaternion neural networks. In the ALOS-2 data, we find a monotonic and nonlinear dependence of the degree of polarization on the incidence angle. Then, we feed multiple-incidence-angle teacher information in the learning process. The distinction results of the proposal present higher accuracy than those of the conventional Wishart distinction and a quaternion neural network without the incidence angle information.