In a nanoplasmonic context, copper (Cu) is a potential and interesting surrogate to less accessible metals such as gold, silver or platinum. We demonstrate optical trapping of individual Cu nanoparticles with diameters between 25 and 70 nm and of two ionic Cu nanoparticle species, CuFe2O4 and CuZnFe2O4, with diameters of 90 nm using a near infrared laser and quantify their interaction with the electromagnetic field experimentally and theoretically. We find that, despite the similarity in size, the trapping stiffness and polarizability of the ferrites are significantly lower than those of Cu nanoparticles, thus inferring a different light-particle interaction. One challenge with using Cu nanoparticles in practice is that upon exposure to the normal atmosphere, Cu is spontaneously passivated by an oxide layer, thus altering its physicochemical properties. We theoretically investigate how the presence of an oxide layer influences the optical properties of Cu nanoparticles. Comparisons to experimental observations infer that oxidation of CuNPs is minimal during optical trapping. By finite element modelling we map out the expected temperature increase of the plasmonic Cu nanoparticles during optical trapping and retrieve temperature increases high enough to change the catalytic properties of the particles.