The proton-lead and lead-lead runs at the LHC are providing an enormous amount of data sensitive to the nuclear modifications of the initial state. The measurements explore a region of phase space not probed by previous experiments opening a possibility to test and, hopefully, also improve the current knowledge of nuclear parton densities. In this talk, we discuss to what extent the present quantitative results for the charge asymmetry in electroweak boson production show sensitivity to the nuclear parton distributions.