In QED, this superposition principle is still valid at least to first order perturbation theory. The deeper reason behind this superposition principle from the QED point of view, is, that photons do not interact with each other. They do not carry charges. They do not "see" each other. So they can be safely superposed without having an effect on each other.
Since the electromagnetic field is described by photons in QED, the same applies for the electromagnetic and therefore also for the electrostatic field.
Please be aware that when I just said that "the field is described by photons" this does not mean that you can imagine a field as composed out of photons. The description happens in a highly non-trivial and very abstract manner totally lacking any imaginability.
As ACuriousMind already pointed out, the field is actually an operator-valued distribution in QED which lives in some Hilbertspace (an abstract mathematical space which kind of replaces the imaginability we are used to in classical physics in QM).
The field operator at a single point in spacetime has the capability of adding or canceling field quanta ("photons" so to speak) at this point in space and time. This capability of adding and canceling quanta at a certain point in spacetime contributes to a transition amplitude if certain condition (like energy momentum conservation) are fulfilled (to formulate it in rather simple language).
One would not talk about "forces" in QED, by the way. The concept of force is nearly totally absent in QED. It is replaced by the concept of interaction (!!!!and not by the concept of exchange of virtual particles!!!!).
You define a suitable interaction term in the Hamiltonian (= energy) or Lagrangian which contains the fields you would like to interact with each other and compute transition amplitudes with it. Regarding the virtual particles, they only appear when you try to compute the transition amplitude via perturbation theory (which is the only suitable way since exact solutions are not available).
So, they are actually kind of artefacts of the approximation scheme we use to evaluate things we can measure at the end.
At the very beginning I said that the superposition principle is valid only to first order perturbation theory. This is true, since when you push the approximation scheme further (to second order), photons indeed can interact with each other. They do not do this directly, but via virtual charged particles. The technical term is "Delbrück scattering". The cross section of this interaction is very, very tiny and does not have an effect in any practical applications.