If I were you I would express my love for the horse and the bond you have. You say you are helping/working in exchange for riding the horse? Or is it in exchange for the actual horse itself?
In that situation I'd see if you could set up a contract working in exchange for payment of the horse. Obviously board could be an issue, but if you two really have such a good relationship she may overlook that. I'd be frank with her... tell her why you want *this* horse, and how much time you can devote to helping her and set a time scale where you'd have him paid off by a certain time.
Say you wanted to pay him off in one year by working for her. $15,000 divided by 52 weeks in a year is $288.00/week. At say, $7.00 an hour you'd have to squeeze in 41.20 hours a week to pay for him. That seems difficult to pull off.
OR, if you worked at $7/hr, 3 hours a day for a year, you'd have about $7644 paid off on his price. You said in a year you could start paying for him.... so if you could squeeze in as much time at her farm, showing her you are really serious about it, and as you said throw in $100 here and there as you can, I feel like that wouldn't be that hard of a thing to do. Provided she is understanding. And anyways, at least I've found that the people you work your ass of for in the horse world are the ones that are more likely to make a deal. Who knows, maybe she'll give him to you for less?
The only thing you can do for sure is be honest about the horse and what you want and why. Tell her your financial situation. Show her your dedication! It can't hurt to try!