But only getting to ride once per week is painful.
You stated that you would need your parents to supply the upfront costs of purchasing the horse and equipment, but that you can handle the long term costs.
So why then don't you
pay for more lessons a week? Put your money toward learning more about horses.
Since you have a desire to be a doctor, let's work a horse example in here.
You have been riding for a couple of weeks. And you now think you are "qualified" to own your own horse. That could very well be the exact same thing as you wanting to jump into college right now at this moment. Or else, only doing one year of college and jumping right into medical school. It just doesn't work that way. You would not be experienced enough for medical school if you only had one year of college. Just like you are not experienced enough with only a few weeks of riding to own your own horse. And even if you do buy a horse, you still need to continue taking lessons.
I know it seems like a time crunch right now, but you have LOTS of time for horses.
I've gone through optometry school and internships. There's no way you can move from rotation to rotation with your horse, and there's no way you have any time for your horse with 80+ hour work weeks. Unless your parents keep the horse for you. So just saying, that you should continue to take lessons for at least a couple years, and then possibly could consider leasing a horse during your time in school (so that you can cut off the lease when you need to move for rotations).
NaeNAe posted a cost example and I"ll post mine too.
Farrier every 6 weeks: Used to be $30 per horse but that will now probably double since my horse now needs special corrective shoeing.
Dentist every year: $120 per horse
Chiropractor every 6 months: $60 per horse
Annual vaccinations: $70 per horse
Dewormers per year: $50 per horse
Grain per year: $150 per horse
Board: $100 per horse
Annual health exam: $300 per horse
Horse trailer monthly payment: $230
Pickup monthly payment: $450 (you need a way to get your horse to and from lessons, right?)
Emergency - horse getting hurt in January: $2,000
Emergency - lameness evaluation last week: $250 + $100 in fuel to get to the specialist. And will need several follow up visits over the next couple months.
Did you think about the emergency stuff? That's where things can really add up in a hurry.
And I know I am forgetting stuff in that price list.