Background: Proton-nucleus collisions have been used as a intermediate baseline for the determination of cold medium effects. They lie between proton-proton collisions in vacuum and nucleusnucleus collisions which are expected to be dominated by hot matter effects. Modifications of the quark densities in nuclei relative to those of the proton are well established although those of the gluons in the nucleus are not well understood. The effect of these modifications on quarkonium production are studied in proton-lead collisions at the LHC at a center of mass energy of 5.02 TeV. Purpose: The possibility of whether the LHC proton-lead data can be described by nuclear modifications of the parton densities, referred to as shadowing, alone is examined. The results are compard to the nuclear modification factor and to the forward-backward ratio, both as a function of transverse momentum, pT , and rapidity, y. Methods: The color evaporation model of quarkonium production is employed at next-to-leading order in the total cross section and leading order in the transverse momentum dependence. The EPS09 NLO modifications are used as a standard of comparison. The effect of the proton parton density and the choice of shadowing parameterization on the pT and rapidity dependence of the result is studied. The consistency of the shadowing calculations at leading and next-to-leading order are checked. The size of the mass and scale uncertainties relative to the uncertainty on the shadowing parameterization is also investigated. Finally, whether the expected cold matter effect in nucleus-nucleus collisions can be modeled as the product of proton-nucleus results at forward and backward rapidity is studied. Results: The rapidity and pT dependence of the nuclear modification factor is found to be generally consistent with the next-to-leading order calculations in the color evaporation model. The forwardbackward ratio is more difficult to describe with shadowing alone. The leading and next-to-leading order calculations are inconsistent for EPS09 while other available parameterizations are consistent. The mass and scale uncertainties on quarkonium production are larger than those of the nuclear parton densities. Conclusions: While shadowing is consistent with the nuclear suppression factors within the uncertainties, it is not consistent with the measured forward-backward asymmetry, especially as a function of transverse momentum. Data from p + p collisions at the same energy are needed.