I’m 16 and I personally would find it so so hard to take care of my pony myself. My parents are such a big help, I’m doing pretty big exams this year and my parents really helped me pay for things when I couldn’t , I’m looking for a job so I can pay for somethings, but personally you should try get your parents help.
I did this at 17, managed to save for many years for the car, bought my horse and I worked my ass off to keep it all afloat.... assuming you are still in school I would advise you to get your parents on board as I would do a 7 hour school day, work for 4 hours and then to the yard. I did this most school days to the point that it made me ill.
Thankfuly my dad picked up the bills for my horse and it allowed me to get back on track with A-levels, however it is not a maintainable lifestyle.
I think that if you say you are willing to contribute but you need your parents to take responsibility for the financial matters.
I know it probably isn’t what you want to hear but there is so much time after school when you have a steady income to have horses.
Hope this helps.