Well.... where to begin. There's so many things when it comes to horses, I hardly know where to start. Basic care for horses doesn't have to be overwhelming. A lot of it can be common sense as well. These are some of the main things you should be concerned about as a horse owner:
(btw, this is all coming out of my head as I go, so if it doesn't make sense just tell me and I'll try to clarify things) ......
1. DIET
- horses are grazing animals and a very large amount of their time is spent eating
- a horse needs (in this order):
A) water
B) grass (not too lush)
C) hay or some form of roughage
D) grain (some form of oats like sweet feed, pellets, etc).
- as for how much, a horse should eat about a rectangular bale of hay a day
- the amount of hay you said she has sounds too little to me
- I also saw the pictures of her and she could put on some weight so you should increase her hay
- make sure she always has fresh clean water to drink
- you can tell if a horse is dehydrated by pulling at the skin on their neck; if it springs back right away without leaving a crease, the horse is fine; if it leaves a lump or fold of skin your horse is dehydrated
- the amount of feed usually depends on the weight of the horse and how much work you doing with her
- the more work you do (as in riding) the more feed she needs to build muscle
- talk to a vet about getting the right feed & amount for your horse, I can't tell you that
- also talk to your vet about possible supplements
- my horse isn't on anything, but some horses need to be
2. HOOVES
- there's a saying that goes, "No hoof, no horse"
- a horse's hooves are very important
- make sure you pick her hooves out carefully every time you are at the barn, looking especially for rocks and large objects around her frog (the "sole" of her hoof)
- rocks stuck in a horse's hoof can make them lame
- your horse needs a good farrier to make sure her feet are in proper condition
- every 6-8 weeks a trim is needed and shoeing, which you are, I'm assuming, from what you have said
- also add a good hoof dressing like RainMaker to your list
- it is applied by a paint-type brush that comes with it and goes on the outside of the hoof (its also good to put it on the frog and up around the coronet band)
- this keeps the hoof from cracking in dry weather
- when you pick her feet, check the outside of her hooves for any cracking
- your farrier is your best friend! :P
3. SHOTS & DEWORMING
- a horse needs yearly shots from the veterinarian to be protected from diseases that affect horses such as rabies, strangles, etc.
- shots are usually done in the spring
- at our barn the vet comes out for one day and gives all the horses at the barn their shots
- besides the regular shots, some horses also get a Coggins test done
- I don't know exactly how it works, but it is needed if you are planning on trailering your horse to another barn (most barns require a coggins for another horse to come on their property) and also when showing
- deworming also needs to be done which helps get rid of worms, bots etc.
- this is usually done about 3-4 times a year and can be administered by an oral paste
- I've actually never dewormed before so I don't know how its done but perhaps you can get someone who knows how to help you
- dewormers come in many forms and brands and it is always a good idea to get a different kind each time to keep the immune system in working order
4. TEETH
- a horse's teeth are also very important
- they tell age and obviously are necessary for eating
- a lot of horse's need to get their teeth floated (or filed) each year
- this keeps them from getting sharp and sore
- talk to your vet and either he or an equine dentist can do the floating
5. GROOMING
- a horse needs and loves to be groomed
- each time you're at the barn, tie your horse to a pole or to crossties and give her a good rub down
- this helps remove dirt and dust and keep her nice and clean
- its nice to brush her mane and tail and make sure they are free of itchy burrs and such
6. OVERALL HEALTH
- you can tell a horse is healthy a lot of times by just watching how they behave and how they look
- a healthy horse will have a clean, shiny coat, clear, bright, interested eyes, they will poop and pee regularly (hehe), drink water, and play around with their friends (as in other horses)
7. EXERCISE
- a horse also needs frequent exercise to be healthy and fit
- even if you don't know a lot about riding right now, don't worry, that will come with time, but your horse still needs to be exercised
- lunging is a great way to exercise a horse without having to ride; its also fairly simple when learned
- make sure though that you ALWAYS walk your horse out thoroughly before stopping (as in, cool her down)
- feel her chest, if she's still really hot, than she's needs to be cooled out more
Ummm.... what else.... it's summer time now and its really hot, so bathing is a nice thing to do. After a ride, if she is really hot you can hose her down with the hose. You'll need a sweat scraper to scrape the water off and make sure she's completely dry before putting her back in the paddock after bathing. Bathing with shampoo should only be done a couple times a year because overuse of shampoo can dull the coat.
Oh, here's another tidbit:
7. HORSE BEHAVIOUR
- I can't go into all the details now but horses have very unique behavioural patterns
- spend a lot of time watching the horses in the field
- which one seems to always get to the hay or grass first and pushes the other one out of the way? (that's a dominant horse)
- which horse stays behind and takes whats left over (that horse is lower on the pecking order)
- horses like to play and will often play halter-tag, rearing and sometimes kicking each other which is normal usually (lol)
- umm ... a horse's ears pinned right back mean she's angry or about to lunge or kick (at another horse)
- horses loves companionship and you will often see them whinnying to each other
- your horse is a mare, so she will also go in heat which is like the human menstrual cycle
- most mares are fine, but some get moody and touchy around this time
- they pee a lot and tend to flirt with the male horses (lol)
Anyway, that's about all I can think up for now and it looks like I wrote an entire novel!

If I think of anything to add, I'll post it later. But good luck and I hope this was helpful! Sorry if its stuff you already know

but I thought I'd start from the real basics.
Oh and one thing I should add ...
8. HORSES ARE FUN!!
K, I'm done. :P