Not to put too fine a point on it, but taking the example posted at the top of this thread specifically....
The model of the robe is in this case incompatible with the horse. As can clearly be seen in the screenshot, the robe seems oriented to the ground level, not the position the robe would be if worn on the body (i.e. head/neck oriented). As such, it's appearing at ground level rather than hanging off the rider's body as one would expect.
To repeat, the mounted horse is a different phenotype (think fat vs. skinny) for the character models. There's no way that NWN provides that I'm aware of to have one object riding another. When mounted, the rider and the horse are one creature, and that creature is the PC that has the appearance of being mounted on a horse.
Just like some of the clothing customizations do not work on all racial and gender phenotypes, so too do some of the customizations not work on the mounted horse phenotypes.