See paper for full list of authors,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 proton-induced dielectron radiation 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 Pee<0.8 GeV/c a strong modification of the shape of the spectrum, which we attribute to an additional ρ-like contribution and a decrease of ω yield. These opposite trends are tentatively interpreted as a strong coupling of the ρ meson to baryonic resonances and an absorption of the ω meson, which are two aspects of in-medium modification of vector mesons. The QCD vacuum is characterized by nonzero expectation values of various quark and gluon operators. Most notable is the finite chiral quark condensate, signaling the spontaneous breaking of chiral symmetry. In a cold strongly interacting medium, the chiral condensate is expected to be modified (in linear density approximation, by about 30% at nuclear saturation density). As predicted by various models [1], [2], [3], [4], [5], [6], [7], [8] and [9], vector meson properties should be affected by changes of the condensates. Such phenomena can be studied in leptonic decays of the vector mesons (e.g. V→e+e−, with V=ρ,ω,ϕ). According to [10] the ρ meson is especially sensitive to changes of those condensates which break chiral symmetry (also called chirally odd condensates). In hadronic many-body approaches many hints have been found for a broadening of the ρ meson spectral function in an ambient nuclear medium [5], [6], [11] and [12]. Experimentally, in-medium properties can be studied in heavy-ion collisions (probing hot and dense hadronic matter) or in proton-, pion- or photon-induced reactions on nuclei (probing cold nuclear matter). For recent reviews on medium effects in cold nuclear matter see in particular [6] and [7]. Medium modifications are expected to be stronger in heavy-ion collisions due to the higher densities and temperatures. Measured observables represent an average over the complete space-time evolution of the temperature and the density of the system. On the other hand, in proton-, pion- or photon-induced reactions the system does not undergo a noticeable density and temperature evolution in time hence conditions of the system are better defined. Electron pair (e+e−) decay of vector mesons is an ideal probe for such studies since electrons and positrons are not affected by strong final state interactions. A promising observable is the spectral shape, i.e. the e+e− invariant mass distribution, but also the nuclear modification of the cross section provides valuable information since i...