Magnetic properties of electron-doped La1/3 Ca2/3 MnO3 manganite nanoparticles with average particle size ranging from 12 to 42 nm, prepared by the glycine-nitrate method, have been investigated in temperature range 5-300 K and in magnetic fields up to 90 kOe. Reduction in the particle size suppresses antiferromagnetism and decreases the Ńel temperature. In contrast to bulk crystals, the charge ordering does not occur in all studied nanoparticles, while a weak ferromagnetism appears above 200 K. Low temperature magnetic hysteresis loops indicate upon exchange bias effect displayed by horizontal and vertical shifts in field cooled processes. The spontaneous and remanent magnetization at low temperature shows a relatively complex variation with particle size. The size-induced structural/magnetic disorder drives the La1/3 Ca2/3 MnO3 nanoparticles to a pronounced glassy behavior for the smallest 12 nm particles, as evidenced by large difference between zero field cooled and field cooled magnetization, frequency dependent ac-susceptibility, as well as characteristic slowing down in the spin dynamics. Time evolution of magnetization recorded in magnetic fields after field cooling to low temperatures exhibits pronounced relaxation and a very noisy behavior that may be caused by formation of some collective states. Magnetic properties of the nanoparticle samples are compared with those of La0.2 Ca0.8 MnO3 nanoparticles. These results shed some light on the coupling between charges and spin degrees of freedom in antiferromagnetic manganite nanoparticles.