Myelin is an insulating, multi-lamellar membrane structure wrapped around selected nerve axons. Increasing the speed of nerve impulses, it is crucial for the proper functioning of the vertebrate nervous system. Human neurodegenerative diseases, such as multiple sclerosis, are linked to damage to the myelin sheath through demyelination. Myelin exhibits a well defined subset of myelin-specific proteins, whose influence on membrane dynamics, i.e., myelin flexibility and stability, has not yet been explored in detail. In a first paper [W. Knoll, J. Peters, P. Kursula, Y. Gerelli, J. Ollivier, B. Demé, M. Telling, E. Kemner, and F. Natali, Soft Matter 10, 519 (2014)] we were able to spotlight, through neutron scattering experiments, the role of peripheral nervous system myelin proteins on membrane stability at room temperature. In particular, the myelin basic protein and peripheral myelin protein 2 were found to synergistically influence the membrane structure while keeping almost unchanged the membrane mobility. Further insight is provided by this work, in which we particularly address the investigation of the membrane flexibility in the low temperature regime. We evidence a different behavior suggesting that the proton dynamics is reduced by the addition of the myelin basic protein accompanied by negligible membrane structural changes. Moreover, we address the importance of correct sample preparation and characterization for the success of the experiment and for the reliability of the obtained results.