The "Jeep-Trailer Barbie Horse" is not an actual Barbie horse... that pose was produced by some other company, in several colors. I used to see them all the time in stores, usually with carriages or horse trailers.
The horse you have marked as "Western Barbie Horse" is in fact Sun Runner (I think she has also been seen under the name Suncharm as well), not the horse in the picture you have labeled "Sunrunner Barbie Horse" (I am not quite sure who that is... several horses were made in similar colors, and unless you know the horse has the original tack, finding out who it is can be a challenge).
"Golden Barbie Horse" looks a lot like a really nice non-Mattel horse I saw once, he even has the same tack as the horse I saw, but I can't say for certain whether he is or isn't Mattel. The head is what throws me off... it looks so much like Barbie's horse, Dallas, and I know she came in a pose-able version (if I recall, she was not released that way in the US). Check the inside of the back thighs... most Mattel horses are marked there, and if they aren't marked there, they will definitely be marked somewhere with "Mattel" *.
I am not sure about "White Barbie horse" either... I am really wanting to know if it says Mattel anywhere on it. There were some Barbie horses not released in the US, done in pose-able molds with Dallas like faces, but I have never seen them out of box (I only have ever seen images of them on the boxes, and the horses don't always look like what the box photo shows). I would love to confirm that this was indeed one of them.
If either of the two pose-able horses are marked MII, then they were made by Meritus Industries Incorporated. I know that company made pose-able Barbie-like horses, in palomino and white.
The mare and foal, between the Appaloosa horse and the other mare and foal set in the "Random horses" photo, are Breyer Dapples (Sunny and her mom). The horse on the end, in the same picture, is also a Breyer Dapples, possibly Alexis.
*In fact, if you are ever unsure about a Barbie looking horse, check all over the body for Mattel... very rarely does Mattel not mark items made by them! Not all Mattel horses are Barbie, but at least you will have a clue that it was definitely made by Mattel.
