We report an analysis of low-temperature measurements of the conductance of partially disordered reduced graphene oxide, finding that the data follow a simple crossover scenario. At room temperature, the conductance is dominated by two-dimensional (2D) electric field-assisted, thermally driven (Pollak-Riess) variable-range hopping (VRH) through highly disordered regions. However, at lower temperatures T, we find a smooth crossover to follow the exp(-E0/E)(1/3) field-driven (Shklovskii) 2D VRH conductance behaviour when the electric field E exceeds a specific crossover value EC(T)(2D) = (EaE(1/3)0 /3)(3/4) determined by the scale factors E0 and Ea for the high-field and intermediate-field regimes respectively. Our crossover scenario also accounts well for experimental data reported by other authors for three-dimensional disordered carbon networks, suggesting wide applicability.