The literature on hidden Markov models (HMMs) within the matrix-variate framework remains relatively sparse and has only recently been explored. In this context, two families of matrix-variate HMMs are introduced in this manuscript. These models offer additional flexibility in capturing tail behavior, allowing for better accommodation of atypical observations compared to traditional normal-based approaches. Additionally, the models facilitate the detection of atypical matrices, which is particularly valuable for matrix-variate data where visual detection methods are challenging. A simulation study is outlined to assess their robustness and ability to detect atypical matrices.