So, you need your character's horse to be lame - what would be the most common problems?
Most lameness in horses can be traced to the foot. Their feet and hooves are surprisingly fragile and are weight bearing structures - they're easily damaged. But lameness can also have a number of causes. Here, in no particular order, are the most common:
1. A foreign object "in" the foot. This is more common in shod horses. An object, most often a stone, becomes caught between the central structure of the foot and the hoof wall. If you've ever had a stone in your shoe, you'll understand. A stone or other object can cause dramatic lameness - which usually goes away immediately once the problem is removed. This is why good horsemen don't go out riding without a hoofpick. If the object stays in there too long, though, it can cause a "stone bruise" - an area that remains sensitive for a while.
2. A hoof abscess. Horses kept in humid conditions are particularly prone to infections in the hoof structure. Abscesses cause sudden, severe lameness, but the horse generally recovers quickly. (Stalled horses are also more likely to get them.
3. Pulled muscles. Just like humans, horses can pull or sprain muscles. (Yes, we keep equine ice packs at the barn).
4. Strained, pulled, or torn tendons. If you need a horse out of action for a long time, sprain or strain the suspensory ligament - this can render an animal useless for over a year. (It holds up the back of the fetlock).
5. Stocking up. This is a generalized inflammation that's caused by overwork or by immobilizing a horse for extended periods of time.
6. Thrush. Horse's hooves are prone to infection by thrush (Most kinds of equine thrush will not infect humans, but it can happen).
7. A sore back. Pain in the back can manifest as lameness. If you want to mystify your hero as to why his horse is lame, put the problem in the back. (If you really want a tricky problem, hind end lameness has been known to be caused by soreness in the tail).
8. Cuts, etc. A painful cut can also cause lameness - but is, of course, easy to find.
(There are lots of other causes. These are just the more common ones).