Approaching zero kelvin means that there is a large (approaching infinite)
change in entropy with respect to a change in heat to the system. I perceive this to mean that there is a lack of micro states, even though this COULD be any constant I prefer to think that the discrete nature of energy is indicative that there cannot be an infinitely small
change in entropy with respect to an infinitely small change in heat. I think that this is a point where the approximation we make using calculus fails.
This leads to only a single conclusion in my mind and that is that the micro state must be changing from 0 to 1 for a finite and measure able change in heat resulting in an infinite resultant change whereas any other micro state count for a finite change in heat is a finite value.
So I don't think it is possible to have a zero kelvin system and a dipole since a dipole would require a difference in charge over some distance and I don't believe there are any fundamental particles that are not uniformly charged.
As for very low temperature which I'm sure you are referring let's again look at the fact that the
change in entropy is very large for any small change in heat. Suppose we have a system of charged particles that are equidistant and far enough apart that their gravity and electrostatic forces are essentially balanced. Would you consider them a solid given this relative rigidity?
Now consider a slightly different system where instead of considering gravity as a factor we had some flexible barrier that all of the particles are repulsed by. Wouldn't it make sense that a similar system as the one above would form where the particles would reach some relatively equidistant equilibrium to balance their electrostatic repulsion with respect to the applied forces from the flexible barrier?
So wouldn't it make sense that the volume enclosed by this barrier depends on the pressure that the flexible barrier exerts inward. Which is telling us the magnitude of the forces involved. So then wouldn't it make sense that the greater the forces involved the more energy it would take significantly perturb a particle to cause a significant change in the system. No this isn't entirely true but I think it is a good way to think about solid, liquid, and gas states as ease in which to cause mobility.
For a realistic system things are more complex geometries but I think the same basic idea holds although there is not dimension symmetry and even lower energy perturbations can cause mobility. But even for a polar molecule I want to point out that there are complex geometries involved so you can't treat them as if the electron cloud causes polar symmetry and even solids have constant vibration.