In Kansas, you cannot hold a horse because someone isn't paying you. You can file for abandonment after 10 days of non payment (there has to be a contract) AFTER a certified letter has been mailed and shown to have been recieved, but not answered. Google your states horse laws.
I agree that this sounds like she was free leasing, and there had been plenty of contact between owner and your sister. She could try Itemizing costs and what not but with no formal contract- I think your sis is SOL>
ALSO- Im married to a service member. If this chick is still keeping a horse stateside, that kinda means she has plans to come home at some point...BUT the military pretty much decides when and to where you go and for how long. I hope she's just overseas on a PCS as apposed to a deployment, because most people don't WANT TO BE DEPLOYED> so shame on the poster who called her a crappy owner and suggested hiding the horse- your a winner.
Oh and one more thing, Military members get free legal counsel, so I don't really suggest fighting this, as it wont cost her a thing