We report a novel method for probing the gate-voltage dependence of the surface potential of individual semiconductor nanowires. The statistics of electronic occupation of a single defect on the surface of the nanowire, determined from a random telegraph signal, is used as a measure for the local potential. The method is demonstrated for the case of one or two switching defects in indium arsenide (InAs) nanowire field effect transistors at temperatures T=25-77 K. Comparison with a self-consistent model shows that surface potential variation is retarded in the conducting regime due to screening by surface states with density Dss≈10(12) cm(-2) eV(-1). Temperature-dependent dynamics of electron capture and emission producing the random telegraph signals are also analyzed, and multiphonon emission is identified as the process responsible for capture and emission of electrons from the surface traps. Two defects studied in detail had capture activation energies of EB≈50 meV and EB≈110 meV and cross sections of σ∞≈3×10(-19) cm2 and σ∞≈2×10(-17) cm2, respectively. A lattice relaxation energy of Sℏω=187±15 meV was found for the first defect.