Yeah, grazing isn't actually dangerous. Horses are actually meant to graze. They weren't meant to be eating hay or grain.
Some horses have issues with too much sugar in the grass, but that's the specific horse's issue, not an actual problem with the grass. In the wild that horse would die (founder or whatever), and its genetics would not pass on, leaving the hardier horses to bring in the new generation.
Anywho, as long as she's outside everyday, for most of the day (you want her out as much as possible), she should have no problems with the grass. The danger begins when the horses aren't turned out in the spring (cause the ground is wet and the barn managers don't want the horses putting footprints in their beautiful grass) and then they're turned out finally but they haven't been transitioning properly from scare winter grass to healthier spring/summer grass. It can shock them.
So... look to hay and grass to gain weight. Grain really doesn't do much. Check out smartpakequine.com to find a decent weight gain supplement if you want. Also, she doesn't need to be on vitamins. They probably won't hurt her, but I don't think she actually needs them. You could toss her on MSM or biotin, or a joint supplement or something.
Horse's stomachs constantly produce acid. (Unlike ours). So they need to keep something in there to buffer the acid. If they do not, they can develop ulcers (super painful burns in the stomach lining from the acid burning through). A lot of stalled horses get thrown a few flakes of hay once or twice a day, with some grain, and then you go outside for like 5 hours. Not really the ideal situation.
And get on your research. You have no business owning a horse if you don't even know its feed requirements. That's basic stuff. It leads people to wonder if you'd notice if your horse was lame, or if the tack didn't fit, or if your farrier is doing a good job, or if you'd notice if her teeth needed to be floated (don't trust other people to know for you; half the time they have no idea either). There are a ton of books out there (check out your local library), as well as the Internet (though there are a lot of idiots on the internet).