Spin-polarized scanning tunneling microscopy is employed to study the internal structure of 360° magnetic domain walls in ultrathin Fe nanowires prepared on W(110). They are formed by pairs of winding 180° walls in an increasing external magnetic field. Their width is governed by an equilibrium of exchange and Zeeman energy. In the relevant field range (B≥50 mT) the demagnetizing energy contributes only indirectly via an increased wall width, i.e., a reduced effective anisotropy, and nonlocal effects are negligible.