The motion of the excess proton is understood as a process involving interconversion between two limiting states, namely, the Eigen and Zundel cations. Nuclear quantum effects (NQE) and the organization of the surrounding solvent play a significant role in this process. However, little is known about how these factors can change the limiting state in molecular systems and the physicochemical properties of its surrounding hydrogen-bond environment. In this work we use state of the art ab initio molecular dynamics simulations to examine the role of NQE on the nature of the proton in four hydrogen chloride hydrates. We demonstrate that NQE significantly alter the phase space properties of the proton and that the local electronic structure of the proton is an exquisitely sensitive indicator of the limiting state in each of the crystals. We evaluate both the proton momentum distribution and the proton chemical shifts and demonstrate that deep inelastic neutron scattering and solid-state nuclear magnetic resonance experiments can serve as complementary techniques for probing the quantum nature of the proton in hydrogen-bonding systems. We believe that the rich and insightful information we obtain for these acid hydrates provides a motivation for new experimental studies.