In social sciences, studies are often based on questionnaires asking participants to express ordered responses several times over a study period. We present a model-based clustering algorithm for such longitudinal data. Assuming that an ordinal variable is the discretization of an underlying latent continuous variable, the model relies on a mixture of matrix-variate normal distributions, accounting simultaneously for within- and between-time dependence structures. An EM algorithm is considered for parameter estimation. An evaluation of the model through synthetic data show its estimation abilities and its advantages when compared to competitors. A real-world application concerning preferences for grocery shopping during the Covid-19 pandemic period in France will be presented.