The Landau quantization visible in dI/dV spectra on n-InAs(110) at B=6 T and T=8 K is studied with high spatial resolution. It is found that the dI/dV intensity is dominated by the Landau bands of the tip-induced quantum dot. The Landau band energies depend on the local surface potential provided by the ionized dopants. Comparison with Hartree-Fock calculations show that the energy shifts are accompanied by an enhanced spin splitting of the Landau bands induced by the spatially varying spin polarization of the dot. Imaging of the spin splitting demonstrates the nonsimple dependence of the spin polarization on the local potential.