So, I don't know if it really counts as "sprites" since they are more "avatar components", and as such I don't know if they would even really qualify for the Spriters Resource. Still, the stuff I saved I think is still pretty cool, and is at least worth showing off:
So, something to note about the skeleton horses, an item called Knell of the Bells, I wasn't able to properly separate the components. That is, the foreground horse is a separate part from the background horse, and so part of the background horse is actually covered by the foreground one.
I dunno how Gaia Online runs their avatar builder, but I think it probably assembles the avatars server side, so the individual parts are not accessible as resources to the client. Generally I've just been taking advantages of glitches where parts of the base model are invisible, or using certain items that remove parts, then just puzzle piecing the non-covered parts of objects together in GIMP. Not a great solution, but it's the best I can do.
EDIT: So, I learned about a few glitches that remove foreground components, so I managed to isolate the background horse.