As Running Bill said, start by worming your horse, you can get a good paste wormer from a feed store. Different wormers have different components to them, so rotated the type of wormer every 4 to 6 weeks for about 3 or 4 doses. This way the worms won't get immune to the wormer and doing it so often, for 3 or 4 doses, assures that you will get the worms at all stages of life. Unless your horse will be around outside horse, going to shows or trail rides with unknown horses, I would worm about three to four time a year.
All horses drop grain on the ground or back into the bucket when they eat, that's not a good test for someone new to horses. But do have the teeth checked and floated by a Vet, they get hooks and points on them that make it painful for the horse to eat. They will lose weight and could colic and die if not kept up. This should be done every couple of years. If you have male horse Gelding or Stallion have the Vet clean the sheath while your horse is on drugs (sedation). If stallion: geld while on drugs!
I agree that a gallon of grain is too much for a horse on pasture, I would give him/her a couple of hand fulls of a "dry cob" or "all feed" twice a day, again you can get this at your feed store for about 5 to 10 dollars for 50lbs.
Sounds like a lot to start with, but it will more than likely get your horse on the healthy track and make him or her alot more fun to work with.
Alan
