The magnetic properties of Co (D=15 nm, L=130 nm) nanowires are reported. In oxidized wires, we measure large exchange-bias fields of the order of 0.1 T below T~100 K. The onset of the exchange bias, between the ferromagnetic core and the antiferromagnetic (AFM) CoO shell, is accompanied by a coercivity drop of 0.2 T which leads to a minimum in coercivity at ~100 K. Magnetization relaxation measurements show a temperature dependence of the magnetic viscosity S which is consistent with a volume distribution of the CoO grains at the surface. We propose that the superparamagnetic fluctuations of the antiferromagnetic CoO shell play a key role in the flipping of the nanowire magnetization and explain the coercivity drop. This is supported by micromagnetic simulations. This behavior is specific to the geometry of a one-dimensional system which possesses a large shape anisotropy and was not previously observed in zero-dimensional (spheres) or two-dimensional (thin films) systems which have a high degree of symmetry and low coercivities. This study underlines the importance of the AFM superparamagnetic fluctuations in the exchange-bias mechanism.