Incoherent neutron scattering by water confined in carbon nanohorns was measured with the backscattering spectrometer SPHERES and analyzed in exemplary breadth and depth. Quasielastic spectra admit δ-plus-Kohlrausch fits over a wide q and T range. From the q and T dependence of fitted amplitudes and relaxation times, however, it becomes clear that the fits do not represent a uniform physical process, but that there is a crossover from localized motion at low T to diffusive α relaxation at high T. The crossover temperature of about 210 to 230 K increases with decreasing wave number, which is incompatible with a thermodynamic strong-fragile transition. Extrapolated diffusion coefficients D(T) indicate that water motion is at room temperature about 2.5 times slower than in the bulk; in the supercooled state this factor becomes smaller. At even higher temperatures, where the α spectrum is essentially flat, a few percentages of the total scattering go into a Lorentzian with a width of about 1.6μeV, probably due to functional groups on the surface of the nanohorns.