To install these, open the Simply Horses zip file, and insert these images into the "mobs" folder within it. If you are using other vehicle textures, you may need to rename these so they don't overwrite the other ones. It seems that the textures need to all be numbered in sequence to work, so if you delete, for example, cart7, you will need to rename the rest after that, so they maintain the sequence of numbers without gaps (if that makes sense).
If you want to recolour your own, I've recoloured each section so you can see how to do it. You can download the coloured vehicles so you can see how the coloured sections work in game: Cart | Wagon | Vardoo