as soon as you hit him up with a contract like that, I suspect he's going to tell you to come get your horse.
He's offering free care. Id say thanks and leave it at that.
If I was in his shoes and you came to me with a contract and asked me to sign it stating I was legally obligated to to give you free care, I'd tell you to pack sand. Come get your horse and you owe me FMV for each day the horse is here.
I'm with Joe. He's doing you a favor (a huge one) and now you want to obligate him to keep your horse until you can afford to keep it yourself?
If someone came to me with this attitude I'd drag the horse out, hand him the lead rope, and kick both off my property ASAP. That's some nerve.
Here's a novel idea: sell the horse until you can afford to keep it yourself.
Another thing you mentioned that made me curious is that you want a contract to make sure "he doesn't take her away from me".
Well, who really has legal ownership of this horse? If it is you, can you prove it? If he has no ownership interest and you can prove yours, him getting rid of the horse without your consent would be theft. No contract needed. Call the cops and let them deal with it.
However, if he is a part owner, you're going to have to buy him out of his share/interest in the horse if you want to be the only one who has a say about what happens to the horse. And even in that case, if he wants the horse out of his property and care there is nothing you can do about it.