The light vector mesons (rho,omega, and phi) were produced in deuterium, carbon, titanium, and iron targets in a search for possible in-medium modifications to the properties of the rho meson at normal nuclear densities and zero temperature. The vector mesons were detected with the CEBAF Large Acceptance Spectrometer (CLAS) via their decays to e(+)e(-). The rare leptonic decay was chosen to reduce final-state interactions. A combinatorial background was subtracted from the invariant mass spectra using a well-established event-mixing technique. The rho-meson mass spectrum was extracted after the omega and phi signals were removed in a nearly model-independent way. Comparisons were made between the rho mass spectra from the heavy targets (A > 2) with the mass spectrum extracted from the deuterium target. With respect to the rho-meson mass, we obtain a small shift compatible with zero. Also, we measure widths consistent with standard nuclear many-body effects such as collisional broadening and Fermi motion.