Low Earth Orbit (LEO) satellite networks are capable of improving the global Internet service coverage. In this context, we propose a hybrid beamforming design for holographic metasurface based terrestrial users in multi-altitude LEO satellite networks. Firstly, the holographic beamformer is optimized by maximizing the downlink channel gain from the serving satellite to the terrestrial user. Then, the digital beamformer is designed by conceiving a minimum mean square error (MMSE) based detection algorithm for mitigating the interference arriving from other satellites. To dispense with excessive overhead of full channel state information (CSI) acquisition of all satellites, we propose a low-complexity MMSE beamforming algorithm that only relies on the distribution of the LEO satellite constellation harnessing stochastic geometry, which can achieve comparable throughput to that of the algorithm based on the full CSI in the case of a dense LEO satellite deployment. Furthermore, it outperforms the maximum ratio combining (MRC) algorithm, thanks to its inter-satellite interference mitigation capacity. The simulation results show that our proposed holographic metasurface based hybrid beamforming architecture is capable of outperforming the state-of-the-art antenna array architecture in terms of its throughput, given the same physical size of the transceivers. Moreover, we demonstrate that the beamforming performance attained can be substantially improved by taking into account the mutual coupling effect, imposed by the dense placement of the holographic metasurface elements.