New reading material!
@BrucePerens_K6BP Yes, if I understand your question. If the two horizontal antennas are orthogonal to each other and to the incident wave and you sample them in a phase-coherent manner, then you have all the information you need to fully describe the polarization state of the incident wave.
A useful way of describing that polarization state is with a Stokes vector:
https://en.m.wikipedia.org/wiki/Stokes_parameters
In the setup you describe, you have measured Ex and Ey from which you can calculate I, Q, U, and V.