What's the Gibbs free energy of a reaction at zero temperature and pressure?
$G^\circ = U(0K) = E^{ele}+ZPE$, i.e. the sum of the electronic energy (electrons and nuclei interacting) and the zero point vibrational energy.

You can't use $K=e^{-\Delta G^\circ/RT}$ at 0K because the derivation assumes that a certain amount of thermal energy is available. But you don't need the equation to figure out the relative amount of two molecules. At equilibrium at 0K all molecules are in the lowest possible state.