  We study the propagation of a color singlet q\bar{q} pair undergoing multiple
scatterings in hot and cold QCD matter. The interaction of the dipole with the
nucleus or plasma is described with the McLerran-Venugopalan and Gyulassy-Wang
models respectively. We find identical results when expressed in terms of the
saturation momentum of either the nucleus or the plasma. We compare two kinds
of multiple scatterings, elastic and inelastic with respect to the target. When
allowing the target to scatter inelastically, the difference with the elastic
case is suppressed by a 1/N^2_c factor. We also discuss some implications of
our results in the following situations: the survival probability of quarkonia
in a hot medium, the production of high-p_T heavy mesons in nucleus-nucleus
collisions, and the production of vector mesons in deep inelastic scattering
off nuclei.
