What is their reason for saying no?
These are great ideas! But also listen to what they have to say and acknowledge it. For example, if they say you need better grades, study a lot harder and show them you’re committed. Show them you will do what it takes to get a new horse. Don’t only do things that show how you will be responsible once you get the horse, show them you can be responsible now. Or, make rules! Like if my grade drops to a C, I can’t ride as much as I normally do or something along those lines.
Make a day plan if you are in school make room for homework 📚
List writing of day plans to care for her, cost etc and positive and negative on getting her (add the negatives so they can see how serious you are and that you realise the responsibility)