We investigate magnetotransport through graphene nanoribbons as a function of gate and bias voltage, and temperature. We find that a magnetic field systematically leads to an increase in the conductance on a scale of a few tesla. This phenomenon is accompanied by a decrease in the energy scales associated to charging effects, and to hopping processes probed by temperature-dependent measurements. All the observations can be interpreted consistently in terms of strong-localization effects caused by the large disorder present, and exclude that the insulating state observed in nanoribbons can be explained solely in terms of a true gap between valence and conduction bands.