We report on the magnetic properties and the crystallographic structure of the cobalt nanowire arrays as a function of their nanoscale dimensions. X-ray diffraction measurements show the appearance of an in-plane hcp-Co phase for nanowires with 50 nm diameter, suggesting a partial reorientation of the magnetocrystalline anisotropy axis along the membrane plane with increasing pore diameter. No significant changes in the magnetic behavior of the nanowire system are observed with decreasing temperature, indicating that the effective magnetoelastic anisotropy does not play a dominant role in the remagnetization processes of individual nanowires. An enhancement of the total magnetic anisotropy is found at room temperature with a decreasing nanowire diameter-to-length ratio , a result that is quantitatively analyzed on the basis of a simplified shape anisotropy model.