I think you should take your time with this, Whitney, and do some serious thinking about several possible pros and cons before you jump into anything. Let me explain a little more of what I mean. First of all, I deeply respect and appreciate your daughter's dream of having her own horse. I was only 16 myself when I got my first horse ( he was my birthday present that year) and unlike your daughter, I had FAR LESS experience or knowledge at the time. Being bit by the horse bug can be incredibly painful, and the younger you are when it happens, the harder it often is to cope with. In my case, it hit me when I was still in kindergarten, but it would be another decade before my parents finally decided to move to the country and allow me to have a horse. Until that time, however, we mainly lived in a series of subdivisions which were near a small college town in the Midwest. It was frustrating as all get out for me when I was young, to see and know people around me who had horses and not have one myself. So yes, I completely understand where your daughter is coming from here, because I've been there and done that.
Now, about the larger question of whether your daughter is ready for the responsibilities that come with horse ownership. It sounds to me like she may be. She also sounds like she's very committed to the idea of being an owner, and wants to make it happen- but in the right way. She's not whining or begging- it's obvious from your description of her that she's done her homework and some market research. She's also made a rather impressive effort to address the financial side of the equation, too, which is unusual in someone her age. Most teenage girls who are horse crazy generally don't think much about what owning a horse will cost, nor do they stop to consider the level of responsibility that's required to properly care for a horse. I think the real issue is going to shift from her to you and your husband. If the two of you feel that your daughter is mature enough and responsible enough to have a horse of her own, then you should work with a professional and get her one. I use that phrase "work with a professional" for a reason. As first time horse buyers/owners, there are a LOT of potential traps and pitfalls that you can easily get into, and having your daughter's trainer or another seasoned horse professional help you in your search is extremely important, for everyone's safety and protection. Buying a horse is NOT like buying a car, where you have the benefit of warranty protection and the ability to take legal action against the seller or dealer if things don't work out. No, getting a horse requires a very different mindset. You have to know what you want, and know how the market works. You also have to know what to AVOID. DON'T TRY to buy a horse on your own without professional guidance and help, no matter how much your daughter might want or try to beg you to. It will only lead to disaster, as I know from experience.
On the subject of money and horse ownership: The actual purchase price is just the tip of the iceberg when it comes to costs. Most of the money that horse owners spend on their animals is for upkeep, not for purchasing. And there are ways to economize on some of the costs, provided that you have the knowledge to do so. One example that I like to use is annual vaccinations. I live on a farm, and we currently have 7 horses. We do all our own shots ourselves each spring. This saves us hundreds of dollars, because we avoid the expense of having to pay the vet for a farm call. It's perfectly legal in my state for lay persons ( non-medical professionals) to give horses vaccines, dewormer, and other medications. We order the vaccines from one of the vet supply houses, along with the syringes/needles to administer them. A complete set of spring shots costs about $75 per horse. This includes all the core vaccines, plus additional vaccines that our vet has recommended to us. Once the horses get their shots each spring, they're good to go until the following year. Coggins tests are another thing you can save money on. You have to have a vet do this, but it's not necessary to do it every year UNLESS you're planning on showing or competing with your horse. If your horse is living at home in a closed herd, away from other strange horses, then Coggins testing is a moot point and not required. Your daughter can learn to do other kinds of routine care, too, instead of relying on a vet to do it. Worming, for example, is something that she needs to learn to do herself. There is absolutely NO REASON to waste money on a farm call from the vet, just to have him or her give the horse a tube of wormer. Wormer can be purchased at most feed and farm supply stores, and many tack stores also sell it. And it would be good for your daughter to learn how to clean her own horse's sheath, if she gets a gelding. Sheath cleaning is part of proper management, and horse professionals routinely do this themselves. I've done it lots of times, with my own geldings. As long as you're gentle and your horse trusts you, you can do it safely without risk if you know how. I'd also do some checking around and find out if there are any equine DENTISTS practicing in your area, and rather than calling a vet, I'd make use of their services. Dentists charge a lot LESS than most vets do, for the same services like routine floating and checkups. So these are some basic examples of ways in which you can save money on costs. Things like tack and equipment are usually one time expenses, provided that you take the time to invest in quality equipment that will last. Likewise, you can keep from having to spend money on things like halters if you buy top quality the first time and your daughter learns to TAKE CARE of what she has.
Worrying about what will happen if the horse gets sick or hurt is like worrying about the weather, Whitney. Of course, it's always a good idea to be prepared for emergencies, but obsessing over how you'll pay for every little detail is pointless and serves no purpose. You can and should look into the possibility of insurance for the horse after you make your purchase. Yes, there are several companies that write insurance policies for horses, but what these policies cover and their costs tends to vary widely by place and by type. Some of the terms that the companies use are a bit confusing, too. There are differences, for example, between major medical insurance, and say, mortality insurance. Be sure that you READ any insurance contract thoroughly and understand all of its language before you sign anything. Another way to reduce your level of worry over what might happen in the event of illness is to make every attempt you possibly can to buy a horse which is WITHOUT a KNOWN HISTORY of colic or other serious digestive disturbances. And the best way to make that happen is to INSIST on a complete and thorough PRE PURCHASE EXAM before any sale is initiated. Once the check is signed and the horse is delivered, it's too late. Pre-purchase exams need to be done by YOUR OWN VET, NOT THE VET of the seller or dealer. Reputable sellers will not object to your having your own vet do this. If someone does object or tries to tell you that "they just had the horse checked last week/yesterday/last month/ a year ago", then that should raise an immediate and HUGE RED FLAG in your mind. Something's wrong there- the seller is hiding something. Likewise, you and your daughter should be able to do things like show up unannounced at the seller's barn to see the horse a few times before the sale goes through. If the seller doesn't permit this, or gets upset about it, then again, you need to REJECT that horse and look elsewhere. Your daughter needs to RIDE the horse herself at least TWICE, and she also needs to see the SELLER ride the animal at least once or twice prior to any sale. It would also be a very good idea for your daughter's instructor or trainer to get on the horse at least once or twice as well, for the same reason- to be sure that the animal is suitable and a good match for your daughter. When it's time to talk price and terms with the seller ( assuming the horse passes the pre-purchase exam) then ask if the seller will agree to a trial period before the sale is finalized. This is also the time to ask about the horse's health history, and get any and all copies of records that the seller may have. If the horse is registered and has papers, ask about getting the originals of those, too. This is particularly true if the horse is a mare, because there may come a time when you may want to think about breeding her. You also need copies of the horse's pedigree for the purpose of identification. There are certain breed registries, such as the AQHA and the Jockey Club, which use lip tatoos as a means of identification when they accept a horse for registration. If the horse you're buying has one of these, it's important that you know about it and get records of it.
I'll close by saying that the final decision about whether or not your daughter is ready for a horse is up to you. I wish you good luck.