Your local extension service should be able to help you identify what grasses are growing, either with samples you bring in, or by sending you home with a pamphlet so you can play "match the grass". They can also help you find a local agronomist who can come do some soil samples of your pasture to help you learn what you need to do in terms of fertilization and weed control, and some can also do hay testing.
We keep the less-desirable grass from spreading by mowing the long areas before they go to seed. Done judiciously, this works well. If it looks like the same grass the animals gladly eat elsewhere, it's probably somewhere they drop manure, and then won't eat in that area. Dragging the pasture or picking up manure, then mowing can help, as can dividing the pasture up into smaller areas and practicing intensive rotational grazing so they have a small area to graze intensely for a few days, then are moved to a new area. This keeps growth even, prevents the horses from being too picky, and keeps some areas from being overgrazed while others are never grazed. Rotating pastures with other animals such as cattle can also help.
Around here, horses on 24/7 pasture generally get started on hay when they'll eat it. We start offering hay in mid-fall, and the horses generally ignore it or pick at it for awhile, then one day they'll demolish it all and look for more. From that point on, they get hay until spring when the same thing happens-- they'll suddenly abandon the hay entirely and then it's pretty safe to stop feeding it. If your horses are kept in a smaller lot and off the bigger pasture for the winter and spring (very common) then you'll need to reintroduce the pasture slowly. Many people wait until they get a cutting of hay off the pasture in June before running horse on it again. If you have horses prone to obesity or founder, keeping them off early spring grass, off stressed grass (during a drought or after it freezes in the fall) can make a big difference in the health and soundness of the horses. Having your hay tested for sugar content and nutrients is something most people don't do, but again, with an at-risk horse, it's worth doing.
I tend to skip complete feeds and ignore sweet feeds entirely. My horses get either plain oats and a mineral/salt block, or recently I've started feeding them a Ration Balancer instsead of the oats with good results. They get about 1 lb per day at most and look great. Ration Balancers are designed to be used with horses on full-time pasture and grass forage. If you have a hard keeper or an older horse lacking teeth, look into a complete senior feed with forage included, or consider supplementing that horse with soaked alfalfa cubes and/or beet pulp for roughage.
The general rule of thumb for feeding hay is 1-2% of the horse's body weight daily in forage. So a 1000 pound horse needs at least 10 lbs per day. Of course, if the horses still have pasture or a rich feed, they need less than this. A horse in very cold climates or where it's rainy, windy, and cold without much shelter will need a lot more to stay warm. Once temps go below zero, I do free-choice for mine. When it's above that, they seem to do fine with twice daily feedings, as that keeps them eating for a few hours after each feed. What you feed is up for debate-- some feel that a high-quality hay that the horses don't need much of is best, while others feel that a lower-quality hay (of course, still free from mold) is better as the horses can then eat more, which can help prevent boredom, ulcers, etc. It's a case-by-case basis choice you'll need to make. Most pleasure horses who do minimal work all winter do just fine on grass hay with a mineral/salt block and perhaps a small amount of grain/feed. A harder working horse, mare in foal, or older horse may need better hay and alfalfa.
In the past, many horses on full-time pasture did not get extra feed in the winter. If the pasture has good grass on it year-round, you may not need to feed hay unless the weather is especially cold or windy. When I have my horses on my parents' farm with 40 acres of good native grass, they eat very little hay over the winter and stay in good shape. This year there are cattle out on that pasture so mine are going to need hay as their current pasture is about 12 acres, and with 3 horses, that's not enough to sustain them over the winter. They still go out on it, but I would venture there's not much nutrition in the grass that's left, and we'll pull them off soon once the ground freezes hard (which it usually has done by now) and put them in a 4-acre dry lot for the winter to spare the pasture until after we hay it off in late spring.
