The HP and VP really only apply to transmissions in the direction of the main beam of a directional antenna and only then when you are talking about transmissions parallel with a flat ground.
All you can really say is that the E field is normal to the direction of propagation. How would you define VP if the beam were arriving vertically at the ground, for instance? For anything but propagation parallel to the ground, there is an element of Horizontal E field, in fact, even if it was originally launched as perfectly VP. (and vice versa.) It's a geometry thing and can seriously hurt the brain.
It's a real nightmare when you try to consider what happens to a linearly polarised wave, launched from a 'feed' when it spreads out and hits a parabolic reflector. The surface of the reflector is in all sorts of planes and the polarisation that emerges from each point is changed on reflection. This effect is less (through cancellation) when the dish is symmetrical but many dishes have 'offset' feeds (look on the sides of some nearby houses). It is common to use circular polarisation which helps in this respect.