A comprehensive first-principles theoretical study of the electronic properties and half-metallic nature of finite zigzag carbon nanotubes is presented. Unlike previous reports, we find that all nanotubes studied present a spin-polarized ground state, where opposite spins are localized at the two zigzag edges in a long-range antiferromagnetic-type configuration. Relative stability analysis of the different spin states indicates that, for the shorter segments, spin-ordering should be present even at room temperature. The energy gap between the highest occupied and the lowest unoccupied molecular orbitals of the finite systems is found to be inversely proportional to the nanotube's segment lengths, suggesting a route to control their electronic properties. Similar to the case of zigzag graphene nanoribbons, half-metallic behavior is obtained under the influence of an external axial electric field.