We report on the nuclear dependence of transverse single-spin asymmetries (TSSAs) in the production of positively charged hadrons in polarized p^{↑}+p, p^{↑}+Al, and p^{↑}+Au collisions at sqrt[s_{NN}]=200 GeV. The measurements have been performed at forward rapidity (1.4<η<2.4) over the range of transverse momentum (1.8