We report on magnetotransport measurements of nanoconstricted (Ga, Mn) As devices showing very large resistance changes that can be controlled by both an electric and a magnetic field. Based on the bias voltage and temperature-dependent measurements down to the millikelvin range we compare the models currently used to describe transport through (Ga, Mn) As nanoconstrictions. We provide an explanation for the observed spin-valvelike behavior during a magnetic field sweep by means of the magnetization configurations in the device. Furthermore, we prove that Coulomb blockade plays a decisive role for the transport mechanism and show that modeling the constriction as a granular metal describes the temperature and bias dependence of the conductance correctly and allows to estimate the number of participating islands located in the constriction.