What they are wanting you to do is draft a bill for civil court. You would need to contact an attorney and get the correct paper work from them and fill it out. Then you take it back to your county clerk. Next thing you need to do is contact your county constable(he's the only one who can get a seizure order from a judge) and sheriff's department if the horse is out of city limits, if not, then contact your local police.
What you have is a verbal agreement with these people. Since you have paperwork showing you are the owner of the horse all you need to do is show up with your trailer, the sheriff, and if the people you loaned the horse to still don't allow you to pick your horse up, the constable will then place an order of seizure to a judge.
As for the health care and damages that were made to the horse, you will have to pay out of pocket for those bills and then take them to civil court to collect the damages made. It could take days or months. BUT don't lose hope and keep all receipts and make sure to have a veterinarian document the condition of the horse either by taking them with you when you pick the horse up or take the horse straight to the vet after you pick up.
Also, you are allowed to pick this horse up with a police officer if the horse is in plain view from standing off the property. So make sure the horse is in a open pasture or a stall, because if the owners of the land claim that the horse is not on the property and you and the officer cannot see the horse, YOU WILL have to wait for the seizure warrant.
And as other posters said, just go pick the horse up when they aren't there. Or take friends and family with you when you go and these people are home. By law they have to file criminal trespassing on you in order for the police to be called out, that takes paperwork, and by the time that happens, you would have already got your horse and off their property. and BTW, if this horse is in fact yours and you show up with friends and family, I doubt they will put up much of a fight seeing as they are the ones breaking the law.
Keep the faith and good luck. and if you aren't able to be reimbursed after you get your horse back for all the damages, then just take it as a lesson learned. Would you rather wait and take them to court while they are still in possession of this horse and do more damage, or would you rather get your horse and insure he's well? Pick your battles.
DWI which is driving while intoxicated. DUI is a lesser offense depending on what state your in which is usually if you are very close to .08 or sometimes if you are at .08. Some states only give DUI to minors and some states its just a lesser charge. But if you receive a DWI you face much greater penal charges and fines.