We theoretically investigate the D'yakonov-Perel' spin-relaxation properties in diffusive wurtzite semiconductor nanowires and their impact on the quantum correction to the conductivity. Although the lifetime of the long-lived spin states is limited by the dominant k-linear spin-orbit contributions in the bulk, these terms show almost no effect in the finite-size nanowires. Here, the spin lifetime is essentially determined by the small k-cubic spin-orbit terms and nearly independent of the wire radius. At the same time, these states possess in general a complex helical structure in real space that is modulated by the spin-precession length induced by the k-linear terms. For this reason, the experimentally detected spin relaxation largely depends on the ratio between the nanowire radius and the spin-precession length as well as the type of measurement. In particular, it is shown that while a variation of the radius hardly affects the magnetoconductance correction, which is governed by the long-lived spin states, the change in the spin lifetime observed in optical experiments can be dramatic. We compare our results with recent experimental studies on wurtzite InAs nanowires.