We studied the single particle dynamics of water and ice adsorbed in graphene oxide (GO) sponges at T = 293 K and T = 20 K. We used Deep Inelastic Neutron Scattering (DINS) at the ISIS neutron and muon spallation source to derive the hydrogen mean kinetic energy, 〈EK〉, and momentum distribution, n(p). The goal of this work was to study the hydrogen dynamics under 2D confinement and the potential energy surface, fingerprinting the hydrogen interaction with the layered structure of the GO sponge. The observed scattering is interpreted within the framework of the impulse approximation. Samples of both water and ice adsorbed in GO show n(p) functions with almost harmonic and anisotropic line shapes and 〈EK〉 values in excess of the values found at the corresponding temperatures in the bulk. The hydrogen dynamics are discussed in the context of the interaction between the interfacial water and ice and the confining hydrophilic surface of the GO sponge.