  We study the {\it quasi-classical limit} of a quantum system composed of
finitely many non-relativistic particles coupled to a quantized field in
Nelson-type models. We prove that, as the field becomes classical and the
corresponding degrees of freedom are traced out, the effective Hamiltonian of
the particles converges in resolvent sense to a self-adjoint Schr\"{o}dinger
operator with an additional potential, depending on the state of the field.
Moreover, we explicitly derive the expression of such a potential for a large
class of field states and show that, for certain special sequences of states,
the effective potential is trapping. In addition, we prove convergence of the
ground state energy of the full system to a suitable effective variational
problem involving the classical state of the field.
