The low temperature phase of single crystals of Nd$_{0.5}$Ca$_{0.5}$MnO$_3$ and Gd$_{0.5}$Ca$_{0.5}$MnO$_3$ manganites is investigated by squid magnetometry. Nd$_{0.5}$Ca$_{0.5}$MnO$_3$ undergoes a charge-ordering transition at $T_{CO}$=245K, and a long range CE-type antiferromagnetic state is established at $T_N$=145K. The dc-magnetization shows a cooling rate dependence below $T_N$, associated with a weak spontaneous moment. The associated excess magnetization is related to uncompensated spins in the CE-type antiferromagnetic structure, and to the presence in this state of fully orbital ordered regions separated by orbital domain walls. The observed cooling rate dependence is interpreted to be a consequence of the rearrangement of the orbital domain state induced by the large structural changes occurring upon cooling. Comment: REVTeX4; 7 pages, 4 figures. Revised 2001/12/05