The answer, of course, partially depends on the size of the horse.
The official world high jump record for a full sized horse is 8 feet and 1 1/4 inches, which has stood since 1949. (The horse that holds it was named Huaso).
Most full sized horses can jump 2'6 and most ponies can manage 2'. (The horses you see routinely jumping 4 and 5 foot fences are both specially bred and specially trained for the task, and have riders that know what they're doing.
Incidentally, mules are jumped differently - from a standing start and without a rider (Horses struggle to jump from a standing start and generally find it easiest to jump from a canter). The record height for a mule "coon jumping" is 6 feet.
This horse is competing in a Puissance competition - a test of pure jumping height traditionally conducted over a wall (the fence is not as solid as it looks - each of those top bricks is very light). Image source: Don Carey via Wikimedia Commons. The wall in this shot is 7ft 2in high.