Scanning tunneling spectroscopy (STS) of thin Fe films on W(110) shows that the electronic structure of domains and domain walls is different. This experimental result is explained on the basis of first-principles calculations. A detailed analysis reveals that the spin-orbit induced mixing between minority d(xy+xz) and minority d(z(2)) spin states depends on the magnetization direction and changes the local density of states in the vacuum detectable by STS. As a consequence nanometer-scale magnetic structure information is obtained even by using nonmagnetic probe tips.