Chanda on horseback...now there's a funny image.
OK, my understanding of the problem is that this is something that is a model issue with some of the clothing customizations and also with the way rideable horses actually work. Mechanically speaking, you are not actually riding a horse creature, but changing the phenotype of your own PC to appear as your character on horseback. When mounted, there's one creature, not two. The some of the clothing models will work with the changes in geometry, but others will not, sadly.
This is kind of a known issue, and I'm not sure if there's a way to "fix" it, but there are ways to work around it. The easiest way is to have a riding outfit. Long robes and dresses are just impractical on horseback anyway.