After a while, I suddenly have this wierd animal skin in my inventory saying its save storage for horse options in hotu or something. Can't drop it. How do I get rid of this? Or is it just a permanet glitch?

That is always there, but meant to be hidden.
If it appeared after you respawned your character, try dragging the skin onto a quick slot and then use the quick slot to re equip it.
That should make it hidden again.

If you think you may have "pickpocketed" the skin off an npc, you can use the console, hit the Tilde key, or in the Talk line, type:
DebugMode 1
runscript nw_itemreset
DebugMode 0
to make the item drop able.

Thank You.

At this point the only way to get rid of it is the method olnorton posted.

To avoid this in future I recommend to download and install community patch 1.72 (there is version for NWN:EE too) as that will fix the issue that causes spawning these skins.