Since the geostationary sat is on the equator and the polarisation is in the equatorial plane, I'd have thought that at any point in the radio field, the polarisation would be parallel to the equatorial plane and all observers would see it locally as polarised parallel to their local plane parallel to the equatorial plane. Whether this is what they call horizontal, I don't know. In this plane a line which is perpendicular to the direction of the satellite will point towards the ground (not vertically), except when the satellite is due south. When the satellite is 90 deg away, I think this line would be vertical, though I don't think the change in angle is linear.
But I don't think we use many satellites more than about 15 deg from south, do we? *I think Cos 15 deg is about 96%, so we are not losing much if we stick to horizontal. Even Cos 30 deg is 86%. Since people align their satellite aerials for azimuth by trial and error with a meter, presumably the pefectionists could do the same with the rotation.
If there is bending of the waves through the atmosphere (which I think is not generally the case with these frequencies) then I suppose the wave might change its plane of polarisation?
*I thought someone had already written that misaligned aerials receive a signal proportional to the Cos of the angle between them. So that it becomes 0 at 90 deg.