There's no substitute for forage, so feed as much as you possibly can. If there is no forage available to you, then you need to get a pelleted forage supplement -- whatever is available in your area. Without some manner of fiber passing through the horse's digestive system the body can't function properly enough to digest and extract the nutrients from whatever else you're feeding. Some type of high fiber forage product needs to compromise 50% or more of the diet to ensure gastric health.
The best type of oil, in my opinion, is soybean -- marketed as vegetable oil. Corn and sunflower oil are higher in omega 6 and 9s, which are pro-inflammatory fatty acids, while some brands of vegetable oil have added omega 3s, or anti-inflammatory fatty acids. Most horse's diets are fairly high in omega 6 and 9s to start, especially horses who get a lot of grain and other concentrated feeds. Sunflower and rice bran oil also tends to be very expensive in comparison to vegetable oil.
Vegetable oil is 100% fat. It's completely empty "cool" calories that the horse's body can digest far easier than concentrated calories/carbs in grain form. One ounce of vegetable oil has 240 calories; one pound of timothy hay has just over 800 calories (the average horse of 1,000lbs requires 15,0000 calories for maintenance -- or over 1.5% of their body weight in forage).
Oil can be safely added to the diet at a rate of a few ounces per day, over the course of seven to ten days, starting with one or two ounces for the first day. At the end of the week, or week and a half, the horse should be worked up to eight ounces of oil fed at two intervals -- half a cup in the morning and half a cup at night. It is not uncommon to experience bouts of intestinal upset when introducing fat into the diet, so if your horse begins to have loose stool then back up on the amount you're feeding by a couple of ounces and introduce it at a much slower rate. Nine ounces of vegetable oil a day will provide your horse with an additional 2,000 calories.
ETA: Regarding omega-3/omega-6/omega-9 ratios:
http://www.thehorse.com/free-reports/30006/omega-3-fatty-acids
http://www.thehorse.com/articles/26200/omega-3-fatty-acids-benefit-sport-horse-health
" During his presentation, Newman focused specifically on how the fatty acid fish oil might benefit sport horses. He cited a study conducted by C.I. O'Connor et al. in 2004 that involved 10 mature geldings on an eight-week exercise program. Four horses were supplemented with corn oil and six were supplemented with fish oil at 180 g/day (which delivered approximately 30g /day of omega-3 fatty acids). Researchers then measured and compared the heart rates, packed cell volume (the amount of red blood cells in the bloodstream), insulin concentrations, plasma glucose, and serum cholesterol concentrations of the two groups of horses.
Significant results included:
The heart rates of horses exercising on a treadmill were lower with fish oil than with corn oil. "This is important to consider with endurance horses," said Newman.
Insulin, plasma glucose, and serum cholesterol levels all were lower in horses fed fish oil."
http://www.thehorse.com/articles/29682/omega-basics-easy-as-1-2-3