Even if my answer is probably a few years too late, maybe it will still help someone. As I have now found out and broke my 8-year-old save while trying it out, it is not because of the graphics options. I tried everything possible with the graphics options, but my skins were always loaded correctly. Until I remembered that I installed the free HD texture pack that Codemasters offered at the time. I then started Grid Autosport on my old laptop where the HD textures are deactivated for performance reasons. And that's the core of it. Apparently Grid Autosport is only able to load my high resolution skins when the HD texture pack is installed. Without the HD texture pack, the game only loads the low-resolution textures, which I usually don't use for my skin pack. The problem now is that Codemasters has removed the game from the Steam Shop, and so has the DLC. Even if they were free. Even though probably only 5 people including me are still playing Grid Autosport, I will probably make a lower resolution skin pack available so that players who buy a Grid Autosport key now can also enjoy the skins.
Thanks for your rating! Every Honda takes a month of skinning, so enjoy with them. More BTCC skins are in work, but it needs a little time. ;) And your Engstler WTCC BMW is not forgotten. ;)