Controlling electron spins strongly coupled to magnetic and nuclear spins in solid state systems is an important challenge in the field of spintronics and quantum computation. We show here that electron droplets with no net spin in semiconductor quantum dots strongly coupled with magnetic ion or nuclear spin systems break down at low temperature and form a nontrivial antiferromagnetic spatially ordered spin texture of magnetopolarons. The spatially ordered combined electron-magnetic ion spin texture, associated with spontaneous symmetry breaking in the parity of electronic charge and spin densities and magnetization of magnetic ions, emerges from an ab initio density functional approach to the electronic system coupled with mean-field approximation for the magnetic or nuclear spin system. The predicted phase diagram determines the critical temperature as a function of coupling strength and identifies possible phases of the strongly coupled spin system. The prediction may arrest fluctuations in the spin system and open the way to control, manipulate, and prepare magnetic and nuclear spin ensembles in semiconductor nanostructures.