We present a detailed magnetic study of the perovskite manganite Pr0.7Ca0.3MnO3 at low temperatures including magnetization and a.c. susceptibility measurements. The data appear to exclude a conventional spin glass phase at low fields, suggesting instead the presence of correlated ferromagnetic clusters embedded in a charge-ordered matrix. We examine the growth of the ferromagnetic clusters with increasing magnetic field as they expand to occupy almost the entire sample at H ~ 0.5 T. Since this is well below the field required to induce a metallic state, our results point to the existence of a field-induced ferromagnetic insulating state in this material.