Abstract : We present data on dielectron emission in proton induced reactions on a Nb target at 3.5 GeV kinetic beam energy measured with HADES installed at GSI. The data represent the first high statistics measurement of dielectrons radiated from cold nuclear matter in a kinematic regime, where strong medium effects are expected. Combined with the good mass resolution of 2%, it is the first measurement sensitive to changes of the spectral functions of vector mesons, as predicted by models for hadrons at rest or small relative momenta. Comparing the e+e- invariant mass spectra to elementary p+p data, we observe for e+e- momenta P<0.8 GeV/c a strong modification of the shape of the spectra, which we attribute to an additional rho-like contribution and a decrease in omega yield. These opposite trends are tentatively interpreted as a strong coupling of the rho meson to baryonic resonances and an absorption of the omega meson, which are two aspects of in-medium modification of vector mesons.