Are you paying for lessons yourself? If you only have lessons once a week, you could find a job somewhere else, and work somewhere else, all while helping your family and doing what you love. Once you turn 14 you can legally work anywhere (at least in Sask, don't know about where you live)
If your lessons are not expensive, you could do them if that is what you really love.
I don't think I could ever get rid of my horse, or stop doing what I love, I would find a way to make it work, even if it means working 7 days a week to keep my horse and to help my family (I am 15)