We show that for Drell-Yan events by unpolarized hadronic projectiles and nuclear targets, azimuthal asymmetries can arise from the nuclear distortion of the hadronic projectile wave function, typically a spin-orbit effect occurring on the nuclear surface. The asymmetry depends on quantities that enter also the spin asymmetry in the corresponding Drell-Yan event on polarized free nucleonic targets. Hence, this study can be of help in exploring the spin structure of the nucleon, in particular the transverse spin distribution of partons inside the proton. All arguments can be extended also to antinucleon projectiles and, consequently, apply to possible future measurements involving nuclear targets at the foreseen HESR ring at GSI.