Depends how the leather was treated, and what it is.
If it’s actually veg-tan saddle skirting, that’s different then suade. Rough-out veg tan is just normal skirting used back-to-front.
If it’s not sealed, then it doesn’t matter which side you oil off of, since eventually the oil will penetrate full depth (I’ve made tack using veg-tan leather…really doesn’t matter which side).
If the leather is sealed (which any of the repellants will do), the oil will tend to stay on top and possibly damage your clothes.
When the rough-out slicks out, it can be restored with a bit of sandpaper.
If you do use oil, be careful which one you choose. Pure neatsfoot is traditional, but will darken the leather. Some oils won’t do that (Bee Natural I think won’t?) .