Tactile and embedded sensing is a new concept that has recently appeared in the context of rovers and planetary exploration missions. Various sensors such as those measuring pressure and integrated directly on wheels have the potential to add a "sense of touch" to exploratory vehicles. We investigate the utility of deep learning (DL), from conventional Convolutional Neural Networks (CNN) to emerging geometric and topological DL, to terrain classification for planetary exploration based on a novel dataset from an experimental tactile wheel concept. The dataset includes 2D conductivity images from a pressure sensor array, which is wrapped around a rover wheel and is able to read pressure signatures of the ground beneath the wheel. Neither newer nor traditional DL tools have been previously applied to tactile sensing data. We discuss insights into advantages and limitations of these methods for the analysis of non-traditional pressure images and their potential use in planetary surface science.