  We present an exact Monte Carlo method to simulate the nonequilibrium
dynamics of electron-phonon models in the adiabatic limit of zero phonon
frequency. The classical nature of the phonons allows us to sample the
equilibrium phonon distribution and efficiently evolve the electronic subsystem
in a time-dependent electromagnetic field for each phonon configuration. We
demonstrate that our approach is particularly useful for charge-density-wave
systems experiencing pulsed electric fields, as they appear in pump-probe
experiments. For the half-filled Holstein model in one and two dimensions, we
calculate the out-of-equilibrium response of the current and the energy after a
pulse is applied as well as the photoemission spectrum before and after the
pump. Finite-size effects are under control for chains of $162$ sites (in one
dimension) or $16\times 16$ square lattices (in two dimensions).
