Like with many hobbies (music, dance, sport etc), some children do totally lose interest when they get older, some stop for a while over the teenage/uni years when there is a lot else going on for them (not necessarily the old chestnut of 'she won't care about ponies any more once she discovers boys' but teenagers do have a lot on their plates these days what with exams, saturday jobs, other hobbies and voluntary work/work experience, learning to drive, uni applications and yes, having a social life), some come back to it as adults, for some it remains an abiding passion and pleasure throughout their lives. You know your DD best but even so you are probably guessing which she'll be at this stage.
As blueblue says, owning your own pony is really, really expensive. Take how much you think you'll spend and double it. Plus it is a huge time commitment for you and your DD, a teenager cannot be expected to take responsibility for a large, dangerous, needy animal so no matter how un-horsey you are it will be your responsibility at the end of the day, there are ways to manage this such as using full livery where staff do all the care of the horse, but even then you can fully expect to do a lot of ferrying around, supervision (most yards don't allow un-accompanied children until at least the mid teens), receiving stressful calls and messages ("DPony is hopping lame do you want us to call the vet?", "Vet's been it was just a stone in his foot
", "Vet's bill has arrived it was ££££ when will you pay", "DPony bucked Staff Member off when being exercised this morning should we have the vet back?" are just a selection of ones I've received this week) as well as writing the cheques. I'm not trying to put you off here, I love my ponies very dearly and they are a total joy, ownership is very rewarding, but I am an adult, it's my own money and time I'm spending, I'm not sure it's reasonable to expect that from a non horsey parent.
All horsey girls dream of having their own ponies, and I know you probably feel you'd do anything to make her happy, but I would honestly think hard about whether it is truly practical in money and time terms at this stage. It may be that it's a dream she needs to fulfil for herself as an adult - it's a good motivating factor to do well in school and get a good job anyway
. Lots and lots of horse mad teens don't get their own ponies and it doesn't traumatise them for life or put them off or anything, and it certainly doesn't mean they can't enjoy riding as a hobby in the meantime. For a fraction of the cost and commitment of horse ownership, can she do lots of being a yard helper, own-a-pony/pony club days, clinics, mini competitions, maybe explore a part-loan or share (some riding schools do these with the school ponies which is a really nice way to ease in as a non-horsey parent as a lot of the care and supervision is then included in the price)? If her riding school doesn't do these can you look at occasionally taking her to a bigger school which does?
Happy to answer any questions and post approximate costs if that would help you?