  We consider the probability distributions of the subsystem (staggered)
magnetization in ordered and disordered models of quantum magnets in D
dimensions. We focus on Heisenberg antiferromagnets and long-range
transverse-field Ising models as particular examples. By employing a range of
self-consistent time-dependent mean-field approximations in conjunction with
Holstein-Primakoff, Dyson-Maleev, Schwinger boson and modified spin-wave theory
representations we obtain results in thermal equilibrium as well as during
non-equilibrium evolution after quantum quenches. To extract probability
distributions we derive a simple formula for the characteristic function of
generic quadratic observables in any Gaussian theory of bosons.
