Pasture only. Hay only. Alfalfa vs. grass. Beet pulp. Ration balancers. Pelleted feed. Sweet feed. Cereal grains. Fats. Supplements.
The options are endless. So how do you decide what and when to feed your horse?
Horses are designed to eat small amounts often throughout the day. Their stomachs continually produce acid, regardless of when they last ate. Because of this, horses that go for long periods of time without any forage are prone to ulcers. It is important that they have constant, or near constant access to grazing or hay. Slow feeders and small mesh hay nets allow the horse to eat less hay while being more satisfied, because it takes longer to eat. They need 1.5-3% of their body weight daily in dry matter forage. This means that a horse would need to consume more pasture than hay, because fresh grass has a much higher water content.
Choosing the right hay is an important part of the feeding process. Based on where you live, it might be easier and cheaper to get grass hay than alfalfa, and vice versa. Alfalfa has several benefits, including a higher calorie count, lower NSC (starches), and is a natural buffer for stomach acid. It has a higher protein content than grass hay, which might be a positive or negative, depending on the horse and what else the horse gets. Alfalfa also has some drawbacks, including a high calcium level (which can adversely affect growing horses if it's the only source of forage), the risk of blister beetles if the hay was not put up properly, and some people believe it makes a horse "hot" (even though I've never had it happen).
There are many types of grass hay; timothy, coastal, bermuda and brome are some examples. Grass hay doesn't present the risk of developmental orthopedic disease that alfalfa does to growing horses, but it's generally lower in energy, lysine, and magnesium than alfalfa. That can be good or bad, depending on the situation. For horses that are hard keepers, I like to feed them all the grass hay they want, and supplement that with alfalfa a few times a day.
Since the quality of hay and pasture varies so much, the only way to be sure what nutrients your horse is getting is to have it tested. If you live in the United States, your local county extension agent should be able to assist you. If it is lacking in nutrients (and most are), you have several options to supplement the diet.
When it comes to concentrated feed, there are many schools of thought. Traditionally, a person would feed oats, corn, and/or barley. Recent research has shown that this is not the healthiest way to feed due to the high sugar/starch content of cereal grains. If you do decide to use one, for whatever reason, oats are the healthiest choice.
Sweet feed has long been popular for it's palatability, however it does contain cereal grains and molasses, which means it's even higher in sugars and starches than straight cereal grains. Many people refer to it as "junk food for horses".
Pelleted feeds are many and varied. The healthiest are based on a fiber source, such as alfalfa or beet pulp, and are fortified with vitamins and minerals. A feed containing soy bean meal will provide adequate amounts of lysine, which is an essential amino acid often lacking in equine diets.
Beet pulp is a fiber with a higher calorie count than most grass hays. It is useful for adding calories to the diet of a hard keeper or underweight horse. It's available as pellets or shreds, with or without molasses. Many people insist that it must be soaked for hours before you feed, and others feed it dry. If your horse bolts down his food, it's best to soak it for at least fifteen minutes, as it can present a choking hazard.
Fat is a good source of calories, especially for hard keepers or those horses on low-starch diets. Flax seed, rice bran, and various oils are all pretty good options, but you should do some research before you choose one.
Ration balancers are great for horses that get enough calories from grazing and/or hay. They just provide the nutrients that might be lacking in a one or two pound per day feeding. They can be found formulated for horses on primarily grass or primarily alfalfa.
You could write a whole book on supplements. The best thing to do is talk to your vet about what else to feed.
Constant access to fresh water and salt are very important.
Here are some resources to help you learn more:
When deciding whether or not your horse needs more calories, check his body condition score. What's Your Horse's Body Condition Score? | Video | TheHorse.com
An easy-to-read book with much more in-depth explanations is Melyni Worth's The Horse Nutrition Handbook
A good website for horses prone to laminitis. Katy Watts | Safergrass.org
Please add any more information or resources as you think of them!