When I free leased horses I didn't pay for anything. The owner provided the horse, feed, farrier, vet etc. I paid for show costs, although there were times when the owner covered those as well.
The reason why? I was providing free board for the owner. The horse got it's stall mucked every day, clean fresh water, fed 3-4x daily, exercise and free training. The owner did not ride as she was working and having health issues- she just wanted her horses to get attention and love while she was busy. She had a lot of animals, and one less was less work for her.
If I had to pay for everything, why bother leasing, if you can just go buy a horse?
If you are in college, the cost of boarding your horse near you will be $300-$500 per month, so even if you cover some of the costs of the horse (like feed or farrier), that is still less than if you end up keeping the horse with you.
I would see if you can find a person to free lease closer to you. That way you can visit the horse, make sure he is well cared for, and maybe cover his feed, or work out a way to take him on rides during weekends.
As a lessee, I would never agree to covering vet costs unless it was due to neglect. If the horse goes lame or gets arthritis, I would not want to be stuck paying for injections on a horse that isn't mine.
Again, there is no point in leasing if I had to pay you , the feed, vet, farrier, and insurance, as well as having to haul home hay/feed and muck stalls. That would eventually add up to being more money than if I actually bought a horse. You may have a hard time finding someone to agree to those terms unless your horse is really spectacular.
I would never send my horse out of state- that is just asking for trouble.
Around here, I could half lease a horse, get lessons and go to shows for a flat monthly fee- without worrying about vet bills, feeding or mucking.
You may have better luck finding someone closer to you if you are willing to cover more yourself.