We study the ground-state properties of kinetic-exchange models for (III,Mn)V semiconductors with randomly distributed Mn ions. Our method is embedded in a path integral spin-wave-type formalism leading to an effective action for Mn spins only with full Matsubara frequency dependence. The zero-frequency contribution to this action is equivalent to static perturbation theory and characterizes the stability of a given spin configuration, while the component linear in frequency can be interpreted as the joint Berry phase of the Mn and carrier system. For simple parabolic-band carriers the collinear ferromagnetic state with all Mn spins in parallel is always stationary but generically unstable. This instability can be characterized in terms of inverse participation ratios and is due to long-ranged nonlocal spin fluctuations. We also present results for the ground-state magnetization as a function of an external field. For carrier dispersions involving anisotropy induced by spin-orbit coupling the collinear state is not even stationary and therefore also not the ground state. This interplay between the anisotropy in the carrier system and the disorder in the Mn positions reflects recent findings by Zarand and Janko [Phys. Rev. Lett. 89, 047201 (2002)] obtained within the RKKY approximation. The stationarity of the collinear state (with the magnetization pointing in one of the cubic symmetry directions) is restored in the continuum or virtual crystal approximation where disorder is neglected.