Ferromagnetic nanowires of Fe have been fabricated by molecular-beam epitaxy on a vicinal W(1 1 0) single-crystal surface with steps along the [0 0 1] direction. The magnetic properties were investigated by Kerr magnetometry. The magnetic easy axis is in the substrate plane and perpendicular to the steps. The remanent magnetization disappears near T_c in a temperature range much narrower than predicted by standard theory of finite-sized systems. Above T_c, the magnetization can be saturated in saturation fields H_s which are small compared to two-dimensional systems.