Temperature-dependent I-V and C-V spectroscopy of single InAs nanowire field-effect transistors were utilized to directly shed light on the intrinsic electron transport properties as a function of nanowire radius. From C-V characterizations, the densities of thermally activated fixed charges and trap states on the surface of untreated (i.e., without any surface functionalization) nanowires are investigated while enabling the accurate measurement of the gate oxide capacitance, therefore leading to the direct assessment of the field-effect mobility for electrons. The field-effect mobility is found to monotonically decrease as the radius is reduced to <10 nm, with the low temperature transport data clearly highlighting the drastic impact of the surface roughness scattering on the mobility degradation for miniaturized nanowires. More generally, the approach presented here may serve as a versatile and powerful platform for in-depth characterization of nanoscale, electronic materials.