Its best to keep all the hairs, mods, and bgs that you are using with the saved SDT character file in one folder. Also, if you were to move a mod, bg, or hair from that original saved folder. It will not load next time around.
What I have is one main folder with the game and other core files I use all the times. (Templates, dialogue checker...) Also in this same folder, I have all my mods/bgs/hairs that I used with my current SDT custom character list. Then with in the main SDT folder, creatr other folders to help separate hairs bgs and other mods. Basically this:
C:\SDT Game - root folder that contains the actual game along with mods/bgs/hairs you use with your custom characters
C:\SDT Game\BGs - keeps background in order
C:\SDT Game\Hairs - keeps hairs in order
C:\SDT Game\Mods - keeps mods in order
This does lead to duplicate files in some case but I find it much easier this way.